Find an explicit formula for the geometric sequence 3,15,75,375,dots.. Note: the first term should be a(1). a(n)=

Identify sequence type: Identify the type of sequence. The sequence 3, 15, 75, 375, ... is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio.Determine first term: Determine the first term (a_1) of the sequence. The first term of the sequence is 3.Calculate common ratio: Calculate the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term: r = 15 / 3 = 5.Write explicit formula: Write the explicit formula for the nth term of the geometric sequence. The explicit formula for a geometric sequence is a_n = a_1 * r^(n - 1). Substitute a_1 = 3 and r = 5 into the formula to get a_n = 3 * 5^(n - 1).

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Find an explicit formula for the geometric sequence
3,15,75,375,dots.. Note: the first term should be
a(1).

a(n)=

Find an explicit formula for the geometric sequence $\newline$ $3,15,75,375, \ldots \text {.. }$ $\newline$ Note: the first term should be $a$ ( $1$ ). $\newline$ $a(n)=$

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Algebra 1

Write variable expressions for geometric sequences

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Q. Find an explicit formula for the geometric sequence

\newline

3,15,75,375, \ldots \text {.. }

\newline

Note: the first term should be

a

(

1

\newline

a(n)=

Identify sequence type: Identify the type of sequence. $\newline$ The sequence $3, 15, 75, 375, extellipsis$ is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio $r$ .
Determine first term: Determine the first term ( $a_1$ ) of the sequence. $\newline$ The first term of the sequence is $3$ .
Calculate common ratio: Calculate the common ratio ( ) of the sequence. $\newline$ To find the common ratio, divide the second term by the first term: $r = \frac{15}{3} = 5$ .
Write explicit formula: Write the explicit formula for the nth term of the geometric sequence. $\newline$ The explicit formula for a geometric sequence is $a_n = a_1 \cdot r^{(n - 1)}$ . Substitute $a_1 = 3$ and $r = 5$ into the formula to get $a_n = 3 \cdot 5^{(n - 1)}$ .