Question

Each sequence has eight terms. Evaluate each related series. 1,-1,-3, . . . . . . -13

Answer 1

The sum of the 8 terms of the series 1-1-3-5- ... -13 is -48

The given sequence is:

1,-1,-3,  . . -13

and there are 8 terms.

The related series of this sequence is:

1-1-3-5- ... -13

Notice that the series is an arithmetic series with:

first term, a(1) = 1

common difference, d = -1 - (1) = -2

last term, a(8) = -13

To find the sum of the series, use the sum formula:

S(n) = n/2 [(a(1) + a(n)]

Substitute n = 8, a(1) = 1, a(n) = a(8) = -13 into the formula:

S(8) = 8/2 [1 + (-13)]

S(9) = 4 . (-12) = -48

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