Question 634284: Find the sum of the first 10 terms of the series defined by the formula:
a(n) = -2n + 5
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First term: Plug in n = 1 and evaluate
a(n) = -2n + 5
a(1) = -2(1) + 5
a(1) = -2 + 5
a(1) = 3
So the first term is 3
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Second term: Plug in n = 2 and evaluate
a(n) = -2n + 5
a(2) = -2(2) + 5
a(2) = -4 + 5
a(2) = 1
So the second term is 1
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Third term: Plug in n = 3 and evaluate
a(n) = -2n + 5
a(3) = -2(3) + 5
a(3) = -6 + 5
a(3) = -1
So the third term is -1
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Keep this pattern going to find the fourth, fifth, ..., eighth, ninth, and tenth terms.
Once you have all 10 terms, add them up to get the sum of the first ten terms.
I'll let you finish.
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Alternate method:
Hint:
Sum of first ten terms = (n*(first term + tenth term))/2
where n = number of terms (which in this case, is n = 10)
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