Respuesta :

Given:The sequence is:

[tex]A(n)=-5\cdot(4^{n-1})\ldots\ldots\ldots\ldots(1)[/tex]

We have to find the first,fourth,eighth term of the sequence.

For first term,put n=1 in equation ..(1).

We get,

[tex]\begin{gathered} A(1)=-5\cdot(4^{1-1}) \\ =-5\cdot(4^0) \\ =-5\cdot1 \\ =-5 \end{gathered}[/tex]

For fourth term,put n=4 in equation (1),

We get,

[tex]\begin{gathered} A(4)=-5\cdot(4^{4-1}) \\ =-5\cdot(4^3) \\ =-5\cdot64 \\ =-320 \end{gathered}[/tex]

For eighth term,put n=8 in Equation (1);

We get,

[tex]\begin{gathered} A(8)=-5\cdot(4^{8-1}_{})_{} \\ =-5\cdot(4^7) \\ =-5\cdot16384 \\ =-81920 \end{gathered}[/tex]

Hence, option (d) is correct.

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