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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!!!!!!!

Respuesta :

gmany

[tex] 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 [/tex]

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:

[tex]a_n=-2\cdot2^{n-1}[/tex]

n=1 substitute into the equation:

[tex]a_1=-2\cdot2^{1-1}=-2\cdot2^{0}=-2\cdot1=-2[/tex]

n=4 substitute into the equation:

[tex]a_1=-2\cdot2^{4-1}=-2\cdot2^{3}=-2\cdot8=-16[/tex]

n=8 substitute into the equation:

[tex]a_1=-2\cdot2^{8-1}=-2\cdot2^{7}=-2\cdot128=-256[/tex]

The answer is C

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