SOLUTION: Determine the value of t1 for an arithmetic sequence, where d = –4 and S14 = 1 120 Ive been having so much trouble trying to figure out how to find t1 without Tn or n. (d= chan

Algebra ->  Sequences-and-series -> SOLUTION: Determine the value of t1 for an arithmetic sequence, where d = –4 and S14 = 1 120 Ive been having so much trouble trying to figure out how to find t1 without Tn or n. (d= chan      Log On


   

Question 1094949: Determine the value of t1 for an arithmetic sequence, where d = –4 and S14 = 1 120
Ive been having so much trouble trying to figure out how to find t1 without Tn or n.
(d= change in each term
S14=sum of the 14th term)
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The formula for the sum of the first n terms of an AP is


S%5Bn%5D = %28a%5B1%5D%2B+%28%28n-1%29%2Ad%29%2F2%29%2An.


At n = 14


S%5B14%5D = %28a%5B1%5D%2B+%28%2814-1%29%2A%28-4%29%29%2F2%29%2A14,   or


1120 = %28a%5B1%5D+-+13%2A2%29%2A14,


which implies  a%5B1%5D+-+26 = 1120%2F14 = 80  ====>  a%5B1%5D = 80 + 26 = 106.

On arithmetic progressions, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.