Find an explicit formula for the geometric sequence 120,60,30,15,dots. Note: the first term should be a(1). a(n)=

Identify sequence type and first term: Identify the type of sequence and the first term. The sequence is 120, 60, 30, 15, ..., which is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. The first term is a(1) = 120.Find common ratio: Find the common ratio of the sequence. To find the common ratio (r), divide the second term by the first term: r = 60 / 120 = 0.5.Write explicit formula: Write the explicit formula for the geometric sequence. The explicit formula for a geometric sequence is a(n) = a(1) * r^(n - 1). Substitute a(1) = 120 and r = 0.5 into the formula to get a(n) = 120 * (0.5)^(n - 1).

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Find an explicit formula for the geometric sequence
120,60,30,15,dots. Note: the first term should be
a(1).

a(n)=

Find an explicit formula for the geometric sequence $\newline$ $120, 60, 30, 15, \dots$ . Note: the first term should be $\newline$ $a(1)$ . $\newline$ $a(n)=$

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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

120, 60, 30, 15, \dots

. Note: the first term should be

\newline

a(1)

\newline

a(n)=

Identify sequence type and first term: Identify the type of sequence and the first term. $\newline$ The sequence is $120, 60, 30, 15, \ldots$ , which is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. The first term is $a(1) = 120$ .
Find common ratio: Find the common ratio of the sequence. $\newline$ To find the common ratio $r$ , divide the second term by the first term: $r = \frac{60}{120} = 0.5$ .
Write explicit formula: Write the explicit formula for the geometric sequence. $\newline$ The explicit formula for a geometric sequence is $a(n) = a(1) \cdot r^{(n - 1)}$ . Substitute $a(1) = 120$ and $r = 0.5$ into the formula to get $a(n) = 120 \cdot (0.5)^{(n - 1)}$ .