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:

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