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?
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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):
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.
