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

Question 1090189: How many terms of the series 4 + 7 + 10 must be taken to give a sum of 531?
Answer by ikleyn(52795) (Show Source): You can put this solution on YOUR website!
.

We have arithmetic progression with the first term  = 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

 = .


Thus we have an equation


 = 531  ====>


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

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


 =  = .


Only positive root makes sense:  n =  = 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".

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