How do I work out this arithmetic sequence?
Q. The 11th term of an arithmetic sequence is 32 and the sum of the first eleven terms is 187. Calculate the 21st term of the sequence?
Asked by Sydney - Fri May 29 11:23:27 2009 - - 5 Answers - 0 Comments

A. From the sum of the first eleven terms, calculate a1 S11 = (11/2)(a1 + 32) = 187 solve for a1 a1 = 2 Now that you know a1 and a11, solve for the difference (d) a11 = a1 + (11 - 1)d 32 = 2 + 10d d = 3 Now, determine a21 a21 = a1 + (21 - 1)d = 2 + 20(3) = 62 The 21st term of the sequence is 62 QED
Answered by the mathemagician - Fri May 29 11:36:57 2009

How do you find 3 numbers in an arithmetic sequence?
Q. I need to know how to find three rational numbers between 2 and 3 to form an arithmetic sequence. Thanks in advance!!!
Asked by MAC-n-CHANEL - Fri Oct 2 21:27:03 2009 - - 1 Answers - 0 Comments

A. This is the formula: an = a1 + (n 1)d d is what you are trying to find. an=3, a1=2, total of numbers in your series is 5 (2,x,y,z,3), which is n. 3=2+(5-1)d 3=2+5d-d 4d=1 d=1/4 ( d stands for difference) so u have 2, 2+1/4, 2+1/4+1/4, 2+1/4+1/4+1/4, 3 which is 2, 2.25, 2.5, 2.75. 3.0. Good luck. Email me if you have further questions.
Answered by Khanh Hung - Fri Oct 2 21:47:23 2009

What is the average (arithmetic mean) of all the even integers greater than 26 and less than 322?
Q. What is the average (arithmetic mean) of all the even integers greater than 26 and less than 322? The answer is 174. Could you please explain WHY because I don't understand how to get to that number.
Asked by Egg Muffin - Thu Apr 17 11:02:04 2008 - - 3 Answers - 0 Comments

A. Average is the result obtained by dividing aggregate of all accounted for by the number of elements considered. Hence it is the number exactly equidistant from either side always. The example case considers 196 numbers in total. This sum ethically has only one defined way to solve. That is taking sum of all the numbers and dividing it by the number of samples in consideration. But practically the result is obtained by adding the first and the last term, and dividing it by 2. Why? As all other numbers can be found equidistant in pairs from this.
Answered by kg7777 - Thu Apr 17 11:33:37 2008

What is the difference between arithmetic and algebraic expressions? Give examples for both of those?
Q. What is the difference between arithmetic and algebraic expressions? Give examples for both of those
Asked by Tacco - Tue Sep 30 13:32:18 2008 - - 2 Answers - 0 Comments

A. Arithmetic is more like doing normal operations, like 3*6, 5-4 Algebra is when you have something like 3x + 4 = 2, something that involves x and you have to solve for it.
Answered by Nae - Tue Sep 30 13:57:33 2008

Why are the arithmetic and geometric means equal when all members of the data set are equal?
Q. The following statement is excerpted from The geometric mean of a data set is smaller than or equal to the data set's arithmetic mean (the two means are equal if and only if all members of the data set are equal). This means if we have a data set [10,10,10]. The arithmetic mean and the geometric mean are really both equal to 10. But what is the theory behind it, making it such a coincidence? Thanks.
Asked by I need answers - Sun Aug 19 01:04:27 2007 - - 3 Answers - 0 Comments

A. No real theory, that's just the way the formulas work. Let's assume we have a set of numbers all the same: (n, n, n, ,n . . . ) and we have y of them. For the arithmetic mean, we add up all y n's and divide by y ny/y = n For the geometric mean, we multiply the numbers together and take the yth root of it. multiplying n over and over again y times is n^y the yth root of (n^y) is n
Answered by douglas - Sun Aug 19 01:16:00 2007

Do the prime numbers admit arbitarily long arithmetic sequences?
Q. More generally, what kinds of sets admit arbitrarily long arithmetic sequences? An arithemetic sequence is just one that is a number plus consecutive multiples of a number. For instance: 5, 9, 13, 17 is a 4 term arithmetic sequence. Here is a 5-term arithmetic sequence in the prime numbers. 5, 11, 17, 23, 29. Clearly you can get long arithemetic sequences. Can you get one that is arbitrarily long? Thank you.
Asked by LivingAlchemist - Fri Jun 27 22:33:06 2008 - - 2 Answers - 0 Comments

A. I may not have understood exactly what you mean. If you are looking for a prime number sieve for primality testing arbitrarily sized integers, the fastest (And the reason that mersenne prime numbers are the largest known primes) is called the Lucas Lehmer primality test for mersenne prime numbers which are in the form of 2^x-1. Sorry if I understood you incorrectly
Answered by Justin M - Fri Jun 27 22:39:01 2008

How is the geometric mean related to the arithmetic mean (approximately)?
Q. Using data for three periods, construct a set of total returns that will produce a geometric mean equal to the arithmetic mean.
Asked by Matt . - Mon Mar 24 18:38:57 2008 - - 1 Answers - 0 Comments

A. I think you have 2 different problems here. One is asking how they are related and the 2nd asking what set of values give an arthmetic mean = the geometric mean. Well they are related in that they are both mathematical statistics and I think I do know one set where they are equal. If the 3 observations each yield the same value then I believe the two means are equal 1+1+1= 3/3 =1 and 1*1*1=1**1/3 = 1. 3+3+3=9/3=3 and 3*3*3=27**1/3=3. If the 3 observations yield different values then it become much more difficult 1+2+3 = 6/3=2 1*2*3=6**1/3=1.817
Answered by muncie birder - Mon Mar 24 20:05:27 2008

How can I generate random arithmetic problems?
Q. about mobile programming with J2ME ,how can I generate random arithmetic problems with single digits and operations + - or * . when a problem is answered whether correctly or incorrectly ,a new problem produced.
Asked by sepide2990 - Tue Nov 25 08:48:55 2008 - - 1 Answers - 0 Comments

A. The algorithm is like this, 1. Generate first random number 1stNum 2. Generate random number from 1-4 to be used as the determiner for the operation 1 = "+", 2="-",3="*", 4="/" 3. Generate second random number 4. Get the answer first to be stored in variable answer 5. Do what you want. Hope this will help
Answered by extreme_pc89 - Tue Nov 25 08:59:40 2008

How is the formula for a arithmetic series discovered?
Q. can someone explain the logic/explanation as to why the formula for an arithmetic series: Sn= n/2(a + tn) is so? if i were to recreate the arithmetic series formula, starting from the sequence formula, how would i do it?
Asked by zeronzero - Sun Dec 14 22:01:23 2008 - - 3 Answers - 0 Comments

A.
Answered by alb9 - Sun Dec 14 22:08:38 2008

An arithmetic sequence has a common difference of 2 and a sum of 120. The first term is numerically equal to?
Q. An arithmetic sequence has a common difference of 2 and a sum of 120. The first term is numerically equal to # of terms. Find all the possible values of the first. Show your work please the answer is 8 btw, but how?
Asked by Paris - Mon Jun 15 21:14:44 2009 - - 1 Answers - 0 Comments

A. OK, so a1=n, and sum = 120 = n/2 (a1+ a1+(n-1)*d) 240=n(2a1+2n-2) 120=n(a1+n-1) 120=n(2n-1) 120=2n^2-n 2n^2 - n - 120 = 0 Solve this quadratic and you have it
Answered by unknown - Mon Jun 15 21:21:26 2009

What are the meanings behind the words "Calculus, arithmetic, geometry, and algebra?
Q. What do these words mean? "Calculus" and "Geometry" mean what ? What do these words describe: Algebra, and arithmetic?
Asked by SuiteLife101 - Fri Jul 11 22:47:27 2008 - - 3 Answers - 0 Comments

A. I believe calculus is the Latin word for pebble, and the origin of the word calculate. Geometry comes from Greek words meaning measure (the -metry part) and earth (the geo- part). Algebra comes from Arabic, but I don't know the details, nor anything about the origins of the word arithmetic, other than the "-metic" part which is also related to "measure". .
Answered by MathMan TG - Sat Jul 12 00:54:57 2008

How do you solve this arithmetic progression Q?
Q. An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, find i) the first term of the series, ii) the smallest positive term of the series. Ps. for i) I got a=397 is this correct?
Asked by Chocolate - Sat Mar 28 06:39:33 2009 - - 3 Answers - 0 Comments

A. Part 1 I hate remembering formulas, so try to think of the sum to n terms as the average of the first and last term multiplied by the number of terms. The first is a, the last is (a+19*7) Sum of the first 20 terms is (a + (a+19*7))/2 * 20 = 530 a=-40 Part 2 -40+(n-1)7 > 0 n > 6.71, meaning the 7th term would give you a positive number: Check the 7th term: -40 + 6*7 = 2 Sounds fine.
Answered by Faz - Sat Mar 28 06:47:59 2009

Can the sum of an arithmetic sequence be negative?
Q. So, can the sum of the arithmetic sequence be negative. Because if ur difference is negative than ur tn will be negative causing you to most likely have a negative sum. Or do you just accept it as positive since a sum shouldnt be negative? Please help. I am just confussing myself here.
Asked by livelovelaugh - Sat Aug 29 23:24:46 2009 - - 2 Answers - 0 Comments

A. Yes. The sum of an arithmetic sequence can definately be negative: Ex: -20, -17, -14, -11, -8... for lets say 10 terms... the sum will be negative b/c there are so many negatives when you add them to the few positives, it still will give you a negative number.
Answered by unknown - Sat Aug 29 23:35:50 2009

how do i solve a sequence that is neither geometric or arithmetic?
Q. i just have a little question about sequences: so i know about arithmetic sequences: a+(n-1)d, and geometric sequences: ar^n-1 but then i come across ones where its neither, but the second differences are the same for example: tn= 0, 4, 12, 24, 40 or tn=3,15,35,63,99 how do i find the general term for those? i know that the second differences are the same, so can i use that to somehow come to an answer? thanks!
Asked by Thea - Thu Sep 18 20:26:54 2008 - - 4 Answers - 0 Comments

A. Greetings, There are a number of ways to do this. One way is as follows... As you said the second differences are constant so the general term will be a quadratic t(n) = an^2 + bn + c, where a, b , and c are constants to be determined, if the third differences were constant then the general term would be a cubic, etc ... Now plug in for 3 values (to get 3 equations for 3 unknowns) t(1) = a + b + c = 0 t(2) = 4a + 2b + c = 4 t(3) = 9a + 3b + c = 12 Then solve the system for a, b, and c a = 2 , b = -2, c = 0 t(n) = 2n^2 - 2n = 2n(n - 1) Similarly, for the next sequence t(1) = a + b + c = 3 t(2) = 4a + 2b + c = 15 t(3) = 9a + 3b + c = 35 a = 4, b = 0, c = -1 t(n) = 4n^2 - 1 = (2n + 1)(2n - 1) Regards
Answered by ubiquitous_phi - Thu Sep 18 20:40:17 2008

How do you solve the following arithmetic sequence questions?
Q. 1) A Formula for the sum of the first n terms is given. Find S subscript n-1 and t subscript n a) Sn=n^2+n b) Sn=2^n-1 c)Sn=2(3^n-1) 2) The number of canis in the row of a triangular display of canned tomatoes form an arithmetic sequence. There are 38 cans in the 3rd row and 17 cans in the 10th row. How many cans are there in the display Please explain your method thoroughly
Asked by bob c - Sun Feb 25 17:00:25 2007 - - 1 Answers - 0 Comments

A. 1) The problem gives you the sum of the first n terms, and asks you to find the corresponding sequence (t_n). First off note that: S_n=t_1+t_2+...+t_n S_{n-1}=t_1+t_2+...+t_{n- 1} So really then, t_n=S_n - S_{n-1} a) Sn=n^2+n S(n-1)=(n-1)^2+n-1=n^2-2n +1+n-1=n^2-n So tn=n^2+n-n^2-n = 2n b)Sn=2^n-1 Sn-1=2^(n-1)-1 So t_n=Sn-Sn-1= 2^n-1-2^(n-1)+1= 2^(n-1) c)Sn=2(3^n-1) Sn-1=2(3^(n-1)-1) So t_n= 2(3^n-1)- 2(3^(n-1)-1)= 2*3^(n-1) 2) We know that an arithmetic sequence is defined recursively as a_{n+1}= a_n +r, with r a given constant Let a_n be the number of cans in the nth row. Then: a_3= a_1+2r= 38 a_10= a_1+9r= 17 So 7r= 17-38= -21 (by subtracting both sides) This gives us r=-21/7=-3 And a_1=a_3-2r= 38+6=44 From there you can… [cont.]
Answered by Yo - Sun Feb 25 17:14:15 2007

Can anyone help solve these problems on an arithmetic series?
Q. The fourth term of an arithmetic series is 3k, where k is a constant, and the sum of the first six terms of the series is 7k+9. (a) Show that the first term of the sequence is 9-8k. (b) Find an expression for the common difference in terms of k. Given that the seventh series of the series is 12, calculate: (c) The value of k. (d) The sum of the first 20 terms of the sequence. Please tell me what each of the values you assign to a letter stand for mean (eg. d means common difference) and, if possible, answer like a typical answer for edexcel a level maths please. First correct answer to the above part (a) will get the points unless someone answers more parts correctly by the end of the evening. Please help and good luck!
Asked by muriel.cameron - Tue Oct 9 10:03:22 2007 - - 4 Answers - 0 Comments

A. The fourth term is given by =a+(4-1)d = a+3d=3k the sum of 6 terms is given by =6/2[2a+(6-1)d] =3[2a+5d] =6a+15d=7k+9 (a+3d=3k)5 5a+15d=15k 6a+15d-5a-15d=7k-15k+9 a=9-8k now sub the value of a in first equation 9-8k+3d=3k 3d=3k+8k-9 3d=11k-9 d=11k-9/3 d=11/3k-3 the seventh term is given by a+(7-1)d=12 9-8k+6(11/3k-3)=12 9-8k+22k-18=12 14k-9=12 14k=21 k=3/2 sub the value of k for a we get 9-8(3/2) =9-12 =-3 the first term a= -3 d=5/2 sum of 20 terms =20/2[2(-3)+19(5/2)] =10[-6+95/2] =10{83/2} =5*83 =415
Answered by math craze - Tue Oct 9 10:38:02 2007

Connection between the slope intercept form and the explicit form of an Arithmetic Sequence?
Q. how are the slope intercept form of a line and the explicit form of an arithmetic sequence connected? What is the correlation between them?
Asked by jesuslives73 - Tue Sep 1 01:17:07 2009 - - 2 Answers - 0 Comments

A. If m is the slope, and c the y-intercept, then the equation of the line is y = m x + c...(1) Then, if c is the first term and x is the common difference of an A.P., its (n)th term y is y = c + ( n-1)x, i.e., y = (n-1)x + c...(2) What strikes you most is the similarity of appearance of these two equations (1) and (2). But that is also the only attribute they have in common. If there is any correlation between them at all, then it must be only ' spurious ' in nature. This is because y in (1) is a continuous variate whereas y in (2) is a discreet variate. Glad To Be Of Help.
Answered by Hemant - Tue Sep 1 01:40:51 2009

Can You Help Me With Arithmetic Series Please ?
Q. The 2nd and 5th terms of an arithmetic series are 26 and 41 respectively. The common difference is 5. The 12th term of the series is 76. Another arithmetic series has 1st term -12 and common difference 7. Given that the sums of the first n terms of these two series are equal, - Find the value of n.
Asked by Vicky S - Tue Nov 18 14:03:17 2008 - - 2 Answers - 0 Comments

A. Arithmetic series formula: a(n) = a(1) +(n-1)d a(2) 26 so: 26 = a(1) +(2-1)*5 26 = a(1) +5 a(1)= 21 we also know 41 = a(1) +(5-1)*5 41 = a(1) +20 a(1) = 21 So there is no contradiction with two bits of information regarding the series. The other series: a(n) = -12 +(n-1)*7 If the sum of the first n terms is equal we will use the sum formula S =n/2*(a(1) +a(n)) or S =n/2*(a(1) +a(1)+(n-1)*d) n/2(42+(n-1)*5)=n/2(-12+( n-1)*7) 42+5(n-1) = -12+7(n-1) 37 +5n =-19+ 7n 2n = 56 n = 28
Answered by Peter m - Tue Nov 18 14:16:03 2008

Can someone help me with arithmetic progressions?
Q. i need help understanding the terms and formulas of arithmetic progresions in general, my teacher kind of wizzed through it in class and i don't really understand. I'd like to know when to use certain formulas i'd like to see how they are written out like in words too, for example when i heard the gauss theory and how he thought of it it really helped. Here are two example questions: 1. Find the sum of all the multiples of three between 1 and 100 and 2. Given that 5 +9+13 +17+...+Un= 2414, find n and Un I think i found the first one ( i got 5049) but i'm really not sure, and the second one i don't know which formula to use.
Asked by gg - Fri Nov 17 16:35:45 2006 - - 1 Answers - 0 Comments

A. For arithmetic progressions, the difference between consequtive terms is a constant. for 1) each will differ by 3 2) each differs by 4, the general form is a0 + (k-1)*d where d is the difference. Btw, for geometric progressions, it's the ratio between terms that's constant, not the difference.
Answered by modulo_function - Fri Nov 17 16:44:30 2006

Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Q. Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Asked by ramos612 - Tue Jul 3 02:02:51 2007 - - 6 Answers - 0 Comments

A. 30/2 * (a1 + a30)
Answered by Dr D - Tue Jul 3 02:06:40 2007