Question

The given series has six terms. What is the sum of the terms of the series?

(–7) + (–9) + (–11) + . . . + (–17)

–32

–42

–72

–52

Answer 1

Given that there are six terms, we have this set:


`a_(n) = \{-7,-9,-11,a_(4),a_(5),-17}\}`

So, we need to find a4 and a5. Given that:

-9-(-7) = -2
-11-(-9) = -2

Then, it is obvious that


`a_(4)-(-11) = -2` ∴
`a_(4)=-13`

`a_(5)-(-13) = -2` ∴
`a_(5)=-15`

Then, the sum of the terms of the series is:


`S = -7-9-11-13-15-17 = -72`