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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.

8,16,32,dots
Write your answer using decimals and integers.

a_(n)=◻(◻)^(n-1)

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. $\newline$ $8,16,32, \ldots$ $\newline$ Write your answer using decimals and integers. $\newline$ $a_{n}=\square(\square)^{n-1}$

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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

8,16,32, \ldots

\newline

Write your answer using decimals and integers.

\newline

a_{n}=\square(\square)^{n-1}

Sequence Type: We have the sequence: $8, 16, 32, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $8, 16, 32, \ldots$ $\newline$ Here, each term is multiplied by a common ratio. $\newline$ The given sequence is geometric.
Determine Values: Determine the values of $a_{1}$ (the first term) and $r$ (the common ratio) of the sequence. $\newline$ First term: $a_{1} = 8$ $\newline$ Common ratio: $r = \frac{16}{8} = 2$
Find Expression: Now that we have $a_{1} = 8$ and $r = 2$ , we can determine an expression to describe $a_{n}$ . Substitute $8$ for $a_{1}$ and $2$ for $r$ into the formula for the nth term of a geometric sequence. $a_{n} = a_{1} \times (r)^{n - 1}$ $a_{n} = 8 \times (2)^{n - 1}$

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