Question

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74

Answer 1

An arithmetic sequence has a constant difference between two consecutive terms.
If the fisrt term is a1, and the nth term is an, then
a1 = a1
a2 = a1 + d
a3 = a2 + d = a1 + d + d = a1 + 2d
a4 = a3 + d = a1 + 2d + d = a1 + 3d
...
an = a1 + (n - 1)d

You are given a1 and a17, and for a17, n = 17. Using the formula above, find d.
Then use the formula again using the d you found and n=27 to find a27.

Answer 2

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