find a6 and an for the arithmetic sequence, when a8=-1 and a10=10

Answer 1

In an arithmetic sequence, the nth term, a_n, is given by the formula a_n = a₁ + (n-1)d, where d is the common difference (the difference between consecutive terms).

So, a₁₀ = a₁ + 9d = 10 and a₈ = a₁ + 7d = -1

We have the system of equations:

a₁ + 9d = 10

a₁ + 7d = -1

Subtracting, we get 2d = 11. So, d = 5.5 and a₁ = -39.5.

Therefore, a₆ = a₁ + 5d = -39.5 + 5(5.5) = -12