Question

Find the first, fourth, and eighth terms of the sequence.

A(n) = −2 ∙ 2x − 1

Answer 1

$A(n)=-2\cdot2^{n-1}\\\\\text{Find the first, fourth, and eighth terms}\\\text{It means}\ A(1),\ A(4)\ \text{and}\ A(8).\\\\\text{Substitute}\ n=1,\ n=4\ \text{and}\ n=8\ \text{in}\ A(n):\\\\A(1)=-2\cdot2^{1-1}=-2\cdot2^0=-2\cdot1=-2\\\\A(4)=-2\cdot2^{4-1}=-2\cdot2^3=-2\cdot8=-16\\\\A(8)=-2\cdot2^{8-1}=-2\cdot2^7=-2\cdot128=-256\\\\\boxed{Answer:\ -2,\ -16,\ -256}$