Question

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

Answer 1

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