Series: Arithmetic Progression Formula Manipulation

Worked Solution:

The formula for the sum, S of n terms of the arithmetic series starting at a whose terms have a common difference of d is:

S =	n (2 a + (n – 1) d ) 2

For this arithmetic series, we have

a =

–  11 4

,

n =

8

and

S =

–  107 2

Rearranging to find d:

d =	2 ( S – a n ) n ( n – 1 )

Using the values for this question we have:

d =	2 ( –  107 2 – ( –  11 4 ) 8 ) 8×7

d =

–  9 8