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  1. 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

  2. [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\\\\\ C. -2;\ -16;\ -256[/tex]

  3. 1.) 8a⁴b³ + 6a²b³ab² - 2a²b³ab

    2.) A. 44

    3.) B. +83 degrees

    4.) D. $0.15

    5.) x⁴ - 256

    6.) D. -122

    7.) -6r²s⁴t³

    Step-by-step explanation:

    1.) To simplify, we simply multiply/distribute and then combine like terms.

    2.) To simplify, we use Order of Operations BPEMDAS to solve.

    3.) To find, we simply subtract 68 and -15 to get +83 as our answer.

    4.) To find, we simply multiply 3 by 24 to get 72, then divide by $410.80 to get $0.15 as our answer.

    5.) To expand/simplify, simply use Difference of Squares to get C. as our answer.

    6.) To find the value, simply plug in 7 for b to get -122 as our answer.

    7.) To find the result, remember that when you divide exponents, you subtract the powers.

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