Answer:
The common difference = 2.
Step-by-step explanation:
An AP can be written as a1, a1 + d, a1 + 2d, a1 + 3d, a1 + 4d, a1 + 5d, a1 + 6d , a1 + 7d.
where a1 = first term and d is the common difference.
Here first term = a1 = 8
3rd term = a1 + 2d = 8 + 2d
5th term = a1 + 4d = 8 + 4d
8th term = 8 + 7d
First 3 terms of a GP are a , ar and ar^2
So from the given information:
a = 8 + 2d
ar = 8 + 4d
ar^2= 8 + 7d
Dividing the second equation by the first we have
r = (8 + 4d)/(8 + 2d)
Dividing the third by the second:
r = (8 + 7d) / (8 + 4d)
Therefore, eliminating r we have:
(8 + 4d)/(8 + 2d) = (8 + 7d)/(8 + 4d)
(8 + 4d)^2 = (8 + 2d)(8 + 7d)
64 + 64d + 16d^2 = 64 + 72d^ + 14d^2
2d^2 - 8d = 0
2d(d^2 - 4) = 0
2d = 0 or d^2 = 4, so
d = 0, 2.
The common difference can't be zero so it must be 2.
