Write a recursive rule for the sequence. Then find a4.

Question

1. -2, -7, -12, -17, ...
2. 2, 9, 37, 149, ...

Answer 1

1. - 2, - 7, - 12, - 17, ...; a₁ = - 2, a_n = a_n-1 - 5, n ≥ 2
2. 2, 9, 37, 149, . . .; a₁ = 2; a_n = 4a_n-1 + 1; n ≥ 2.

Answer 2

For the first sequence, a₁ = -2 and a_n+1 = a_n - 5, for n ≥ 1.

For the second sequence, a₁ = 2 and a_n+1 = 4a_n + 1, for n ≥ 1