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Find an explicit formula for the geometric sequence
12,24,48,96,dots..
Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the geometric sequence $\newline$ $12, 24, 48, 96, \dots$ . $\newline$ Note: the first term should be $\newline$ $b(1)$ . $\newline$ $b(n) =$

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Write variable expressions for geometric sequences

Full solution

Q. Find an explicit formula for the geometric sequence

\newline

12, 24, 48, 96, \dots

.

\newline

Note: the first term should be

\newline

b(1)

.

\newline

b(n) =

Identify Sequence Type: Identify the type of sequence. $\newline$ The sequence $12, 24, 48, 96, extellipsis$ is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio.
Determine First Term and Common Ratio: Determine the first term ( $b_1$ ) and the common ratio ( $r$ ) of the sequence. $\newline$ The first term is $b_1 = 12$ . $\newline$ To find the common ratio, divide the second term by the first term: $r = \frac{24}{12} = 2$ .
Write Explicit Formula for nth Term: Write the explicit formula for the nth term of the geometric sequence. $\newline$ The formula for the nth term of a geometric sequence is $b(n) = b(1) \cdot r^{(n - 1)}$ . $\newline$ Substitute $b(1) = 12$ and $r = 2$ into the formula. $\newline$ $b(n) = 12 \cdot 2^{(n - 1)}$ .

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