SOLUTION: The partial sum in the arithmetic series with first term 17 and a common difference of 3 is 30705. How many terms are there in the series?

Question 1121961: The partial sum in the arithmetic series with first term 17 and a common difference of 3 is 30705. How many terms are there in the series?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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Use the formula for the sum of the first n terms of an arithmetic progression


 =  = .


Substitute the given data to get


30705 = (17+(n-1)*1.5)*n.


Multiply both sides by 2


61410 = 34n +3n*(n-1).


You get a quadratic equation


3n^2 + 31n - 61410 = 0.


Solve it for n


 =  = .


Choose the positive root


n =  = 138.


Answer.  138 terms.

Solved.

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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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Free of charge online textbook in ALGEBRA-II
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