In an arithmetic sequence, the 6th term is 9 and the 8th term is 15

Hopefully the math terms won't confuse anyone.

So in the series, a_6 = 9 and a_8 = 15. Since it's an arithmetic sequence, all the terms in the series can be represented as:

a_n = a_0 + n * k

where n is the nth number. K is a constant you add to reach the next term, and a_0 is the starting constant.

a_6 = a_0 + 6 * k

a_8 = a_0 + 8 * k

solving this system gives you that

k = 3 and a_0 = - 9

for any term n for this arithmetic sequence,

a_n = - 9 + 3 * k