SOLUTION: Consider the arithmetic series 2+9+16+... . Find the number of terms that will give a partial sum of 335.

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Question 1039328: Consider the arithmetic series 2+9+16+... . Find the number of terms that will give a partial sum of 335.
Answer by chen.aavaz(62) About Me  (Show Source):
You can put this solution on YOUR website!
This is an arithmetic sequence with common difference d=(9-2)=7 (we subtract any two subsequent terms).
The nth term is calculated as follows:
an=a1%2B%28n-1%29%2Ad
The sum of the first n numbers is
Sn=%28n%2F2%29%2A%282%2Aa1%2B%28n-1%29%2Ad%29
In our case, Sn=335, a1=2 and d=7,
Therefore:
335=%28n%2F2%29%2A%284%2B%28n-1%29%2A7%29 and by solving the quadratic equation 7%2An%5E2-3%2An-670=0 we get n=10 (by keeping only the positive root).
So the answer is 10 terms.