In an arithmetic sequence, the nth term, an, is given by the formula an = 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
Explanation
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