SOLUTION: How many terms of the series 4 + 7 + 10 must be taken to give a sum of 531?

Algebra ->  Sequences-and-series -> SOLUTION: How many terms of the series 4 + 7 + 10 must be taken to give a sum of 531?      Log On


   

Question 1090189: How many terms of the series 4 + 7 + 10 must be taken to give a sum of 531?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
We have arithmetic progression with the first term a%5B1%5D = 4 and the common difference d = 3.

The number of terms, n, is unknown.


The formula for the sum of the first n terms of any AP is

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


Thus we have an equation


%284+%2B+%28%28n-1%29%2A3%29%2F2%29%2An = 531  ====>


(8 + 3*(n-1))*n = 1062  ====>

3n^2 + 5n - 1062 = 0  ====>


n%5B1%2C2%5D = %28-5+%2B-+sqrt%285%5E2+%2B+4%2A3%2A1062%29%29%2F%282%2A3%29 = %28-5+%2B-+113%29%2F6.


Only positive root makes sense:  n = %28-5+%2B+113%29%2F6 = 18.


Answer.  n = 18,  or  18 terms.

Solved.


There is a bunch of lessons on arithmetic progressions in this site:
    - 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


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".