Question

Write an explicit formula for an the n’th term with the sequence 2, -10,50

Answer 1

This is a geometric sequence with common ratio -5 (since -10/2 = 50/−10 = −5). If a1 = 2 (n starts at 1), the explicit formula is

a_n = 2(−5)^{\,n−1}, for n ≥ 1.

(If you prefer n starting at 0, use a_n = 2(−5)^n.)