Question

help with number 38find the first, fourth, and eighth terms of the sequence

Answer 1

Given:The sequence is:

$A(n)=-5\cdot(4^{n-1})\ldots\ldots\ldots\ldots(1)$

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

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

We get,

$\begin{gathered} A(1)=-5\cdot(4^{1-1}) \\ =-5\cdot(4^0) \\ =-5\cdot1 \\ =-5 \end{gathered}$

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

We get,

$\begin{gathered} A(4)=-5\cdot(4^{4-1}) \\ =-5\cdot(4^3) \\ =-5\cdot64 \\ =-320 \end{gathered}$

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

We get,

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

Hence, option (d) is correct.