Question

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

Answer 1

Answer:

C

Step-by-step 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

Answer 2

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