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Find the sum of the first 25 terms of the sequence \(1, 2, -3, 4, 5, -6, 7, 8, -9, \dots.\)

Mar 5, 2019

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Notice that

1   + 2 - 3 = 0

4 + 5 -   6 = 3

7 + 8 - 9 =   6

So....the first 24 terms will be groups of 3 and there will be 8 of these groups

And the last group will sum to  3(8-1) = 21

So the sum of these 8 groups will be    [ 0 + 21] * (8/2)  =  21 * 4 =  84

And the 25th term = 25

So...the sum is

84 + 25 =

109

Mar 5, 2019
edited by CPhill  Mar 5, 2019
edited by CPhill  Mar 5, 2019
edited by CPhill  Mar 5, 2019