SOLUTION: Find the number of terms and the sum of the series 7+17+27+...+107

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Question 87314: Find the number of terms and the sum of the series 7+17+27+...+107
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
It appears this sequence is an arithmetic one (since we simply add 10 each time to get from term to term).
So the arithmetic sequence would be
a%5Bn%5D=10n%2B7

So plug in a%5Bn%5D=107 to find out how many terms there are:

107=10n%2B7 plug in a%5Bn%5D=107

100=10n Subtract

100%2F10=n Divide

n=10 Reduce

Since we start off at n=0 there are 11 terms

In order find the sum of an arithmetic sequence, simply use this formula

S=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29 where a%5B1%5D is the first term, a%5Bn%5D is the last term, and n is the number of terms

S=%2811%2F2%29%287%2B107%29 Plug in a%5B1%5D=7, a%5Bn%5D=107, and n=11

S=%2811%2F2%29%28114%29 Add

S=627 Multiply

So 11 terms of this sequence adds up to 627