Question

The first term of an arithmetic progression is 8. If the tenth term is double the second term, the common difference is...

Answer 1

8/7

Explanation:

8 + (10-1)d = 2(8 + d)

8 + 9d = 16 + 2d

7d = 8

d = 8/7

Answer 2

d = 8/7.

Explanation:

Formula for the nth term an = a1 + (n - 1)d where a1 = the first term and d = the common difference.

Here we have:

a2 ( the second term) = a1 + (n - 1)d

= 8 + (2 -1 )d = d + 8.

In the same way we can show that the 10th term

a10 = 9d + 8.

But we are given that a10 = 2*a2 so:

9d + 8 = 2(d + 8)

9d + 8 = 2d + 16

7d = 8

d = 8/7.