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

8/7

Step-by-step explanation:

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

8 + 9d = 16 + 2d

7d = 8

d = 8/7

d = 8/7.

Step-by-step 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.