Find an explicit formula for the geometric sequence 96,24,6,1.5,dots. Note: the first term should be b(1). b(n)=

Identify Sequence Type: Identify the type of sequence. The sequence 96, 24, 6, 1.5, ... 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). The first term is b(1) = 96. To find the common ratio, divide the second term by the first term: r = 24 / 96 = 0.25.Write Explicit Formula: Write the explicit formula for the geometric sequence. The explicit formula for a geometric sequence is b(n) = b(1) * r^(n - 1). Substitute b(1) = 96 and r = 0.25 into the formula. b(n) = 96 * (0.25)^(n - 1).

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Find an explicit formula for the geometric sequence
96,24,6,1.5,dots. Note: the first term should be
b(1).

b(n)=

Find an explicit formula for the geometric sequence $\newline$ $96,24,6,1.5, \ldots \text {. }$ $\newline$ Note: the first term should be $b(1)$ . $\newline$ $b(n)=$

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Math Problems

Algebra 1

Write variable expressions for geometric sequences

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Q. Find an explicit formula for the geometric sequence

\newline

96,24,6,1.5, \ldots \text {. }

\newline

Note: the first term should be

b(1)

\newline

b(n)=

Identify Sequence Type: Identify the type of sequence. $\newline$ The sequence $96, 24, 6, 1.5, extellipsis$ is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio $r$ .
Determine First Term and Common Ratio: Determine the first term ( $b(1)$ ) and the common ratio ( $r$ ). $\newline$ The first term is $b(1) = 96$ . $\newline$ To find the common ratio, divide the second term by the first term: $r = \frac{24}{96} = 0.25$ .
Write Explicit Formula: Write the explicit formula for the geometric sequence. $\newline$ The explicit formula for a geometric sequence is $b(n) = b(1) \cdot r^{(n - 1)}$ . $\newline$ Substitute $b(1) = 96$ and $r = 0.25$ into the formula. $\newline$ $b(n) = 96 \cdot (0.25)^{(n - 1)}$ .