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Find an explicit formula for the geometric sequence
2,6,18,54,dots. Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the geometric sequence $\newline$ $2,6,18,54, \ldots \text {. }$ $\newline$ Note: the first term should be $b(1)$ . $\newline$ $b(n)=\square$

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Write variable expressions for geometric sequences

Full solution

Q. Find an explicit formula for the geometric sequence

\newline

2,6,18,54, \ldots \text {. }

\newline

Note: the first term should be

b(1)

.

\newline

b(n)=\square

Identify Sequence Type: Identify the type of sequence. $\newline$ The sequence $2, 6, 18, 54, \ldots$ is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio.
Find First Term and Ratio: Determine the first term $b(1)$ and the common ratio $r$ of the sequence. $\newline$ The first term is $b(1) = 2$ . $\newline$ To find the common ratio, divide the second term by the first term: $r = \frac{6}{2} = 3$ .
Write Explicit Formula: Write the explicit formula for the geometric sequence using $b(1)$ and $r$ . The explicit formula for a geometric sequence is $b(n) = b(1) \cdot r^{(n - 1)}$ . Substitute $b(1) = 2$ and $r = 3$ into the formula. $b(n) = 2 \cdot 3^{(n - 1)}$ .

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