Find the first four terms and stated term given the geometric sequence, with a1 as the 1st term.

an = 6^n-1, a6

an = - 2^n-1, a5

For the first sequence:

The first 4 terms are 1, 6, 36, and 216; a₆ = 7776

For the second sequence:

The first 4 terms are 1, - 2, 4, and - 8; a₅ = 16

Using n as the term number in the first sequence,

a₁ = 6^ (1-1) = 6⁰ = 1; a₂ = 6^ (2-1) = 6¹ = 6; a₃ = 6^ (3-1) = 6² = 36; a₄ = 6^ (4-1) = 6³ = 216; a₅ = 6^ (5-1) = 6⁴ = 1296; and a₆ = 6^ (6-1) = 6⁵ = 7776.

Using n as the term number in the second sequence,

a₁ = - 2^ (1-1) = - 2⁰ = 1; a₂ = - 2^ (2-1) = - 2¹ = - 2; a₃ = - 2^ (3-1) = (-2) ² = 4; a₄ = - 2^ (4-1) = (-2) ³ = - 8; and a₅ = - 2^ (5-1) = - 2⁴ = 16.