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Find the 9^th term of the geometric sequence
2,8,32,dots
Answer:

Find the $9^{\text {th }}$ term of the geometric sequence $2,8,32, \ldots$ $\newline$ Answer:

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Geometric sequences

Full solution

Q. Find the

9^{\text {th }}

term of the geometric sequence

2,8,32, \ldots

\newline

Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant.
Determine Common Ratio: Determine the common ratio $r$ of the sequence. $\newline$ The second term is $8$ and the first term is $2$ , so the common ratio is $\frac{8}{2} = 4$ .
Use Formula for nth Term: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $a_n$ is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Calculate $9$ th Term: Calculate the $9$ th term using the formula. $\newline$ The first term $a_1$ is $2$ , the common ratio $r$ is $4$ , and $n$ is $9$ . $\newline$ $a_9 = 2 \times 4^{9-1} = 2 \times 4^8$
Compute Power of $4$ : Compute the power of $4$ . $\newline$ $4^8 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 65536$
Multiply First Term: Multiply the first term by the result from the previous step. $a_9 = 2 \times 65536 = 131072$

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\newline

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\newline

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\newline

\newline

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\newline

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