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Write an equation to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $\text{–}2, \text{–}8, \text{–}32, \ldots$ $\newline$ Write your answer using decimals and integers. $\newline$ $a_n =$ $\underline{\hspace{1cm}}$ $(\underline{\hspace{1cm}})^{n - 1}$

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Write variable expressions for geometric sequences

Full solution

Q. Write an equation to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

\text{–}2, \text{–}8, \text{–}32, \ldots

\newline

Write your answer using decimals and integers.

\newline

a_n =

\underline{\hspace{1cm}}

(\underline{\hspace{1cm}})^{n - 1}

Sequence Type: We have the sequence: $-2, -8, -32, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $-2, -8, -32, \ldots$ $\newline$ Here, each term is multiplied by a common ratio. $\newline$ The given sequence is geometric.
Values Determination: Determine the values of $a_1$ and $r$ of the sequence. $\newline$ First term: $a_1 = -2$ $\newline$ Common ratio: $r = (-8) / (-2) = 4$
Expression for $a_n$ : We have: $\newline$ $a_1 = -2$ $\newline$ $r = 4$ $\newline$ Determine an expression to describe $a_n$ . $\newline$ Substitute $-2$ for $a_1$ and $4$ for $r$ . $\newline$ $a_n = a_1 (r)^{(n - 1)}$ $\newline$ $a_n = -2(4)^{n-1}$

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