Arithmetic Sequence: Sum of 1st 4 terms, if 6th is 8, 10th is 13

c3ulrich

New member
Joined
Sep 18, 2018
Messages
2
I got this question wrong on an ACT practice test, but it offered no explanation, just the answer.



58. What is the sum of the first four terms of the arithmetic sequence in which the sixth term is 8 and the tenth term is 13?

. . . . .F. 10.5
. . . . .G. 14.5
. . . . .H. 18
. . . . .J. 21.25
. . . . .K. 39.5




I was just wondering if some of you could explain how to solve it the fastest and most efficient way. I would have used the formula S=n(a1+an)/2, but it does not give the first term. Thanks for the help!
 

Attachments

  • Screen Shot 2018-09-18 at 9.47.40 AM.jpg
    Screen Shot 2018-09-18 at 9.47.40 AM.jpg
    18.1 KB · Views: 9
Last edited by a moderator:
I got this question wrong on an ACT practice test, but it offered no explanation, just the answer.



58. What is the sum of the first four terms of the arithmetic sequence in which the sixth term is 8 and the tenth term is 13?

. . . . .F. 10.5
. . . . .G. 14.5
. . . . .H. 18
. . . . .J. 21.25
. . . . .K. 39.5




I was just wondering if some of you could explain how to solve it the fastest and most efficient way. I would have used the formula S=n(a1+an)/2, but it does not give the first term. Thanks for the help!

What about the last term? It's not given either. Instead we are given the 6th and 10th terms.

Here's the secret (you can tell all your friends) - 99% of math problems contain a major hint: there is a reason why you are given every bit of information in the problem statement. If your attempted solution ignores some of it, there is a good chance you are missing something.

You are given:
* the sequence is arithmetic (what does it mean?)
* there are 4 terms
* 6th term is 8, 10th term is 13

You need to use all of the above to obtain what's needed in the sum formula.
 
Last edited by a moderator:
I attempted it again, and got it right. Thanks for the tips. Is this the the best (fastest) way to solve it?

5/4=1.25 (how much it increases each term). 8 - (5)(1.25)=1.75 (first term). (1.75)+(1.75+1.25)+(3+1.25)+(4.25+1.25)=14.5
 
An "arithmetic sequence" has some starting value, \(\displaystyle a\) and a common difference, d. The terms in the sequence are a, a+ d, a+ 2d, a+ 3d, …. In general, the "nth" term is a+ (n-1)d. If "the 6th term is 8" then a+ 5d= 8. If "the 10th term is 13" then a+ 9d= 13. Solve those two equations for a and d so that you can find first 4 terms and add them.
 
Top