Question

Find the first, fourth, and eighth terms of the sequence. A(n) = −2 ∙ 2^x − 1

A. -4; -32; -512

B. -8; -64; -1,024

C. -2; -16; -256

D. 1; -64; -16,384

PLEASE HELP ME!!!!!!!

Answer 1

`a_n=-2\cdot2^(n-1)\\\\n=1\to a_1=-2\cdot2^(1-1)=-2\cdot2^0=-2\cdot1=-2\\\\n=4\to a_4=-2\cdot2^(4-1)=-2\cdot2^3=-2\cdot8=-16\\\\n=8\to a_8=-2\cdot2^(8-1)=-2\cdot2^7=-2\cdot128=-256\\\\Answer:\ C. -2;\ -16;\ -256`

Answer 2

C

Explanation:

The first term is when n=1, the fourth term is when n=4 and the eighth term is when n=8 for equation:

`a_n=-2\cdot2^(n-1)`

n=1 substitute into the equation:

`a_1=-2\cdot2^(1-1)=-2\cdot2^(0)=-2\cdot1=-2`

n=4 substitute into the equation:

`a_1=-2\cdot2^(4-1)=-2\cdot2^(3)=-2\cdot8=-16`

n=8 substitute into the equation:

`a_1=-2\cdot2^(8-1)=-2\cdot2^(7)=-2\cdot128=-256`

The answer is C