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

Determine First Term and Ratio: To find an explicit formula for a geometric sequence, we need to determine the first term (a(1)) and the common ratio (r). The first term is given as 120.Calculate Common Ratio: Next, we need to find the common ratio. The common ratio in a geometric sequence is found by dividing any term by the previous term. Let's divide the second term (60) by the first term (120). r = 60 / 120 = 0.5Write Explicit Formula: Now that we have the first term (a(1) = 120) and the common ratio (r = 0.5), we can write the explicit formula for the nth term of the geometric sequence as: a(n) = a(1) * r^(n-1)Substitute Values: Substituting the values of a(1) and r into the formula, we get: a(n) = 120 * (0.5)^(n-1) This is the explicit formula for the given geometric sequence.

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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. $\newline$ $120, 60, 30, 15, \dots$ $\newline$ Note: the first term should be $a(1)$ . $\newline$ $a(n)=\square$

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Q. Find an explicit formula for the geometric sequence.

\newline

120, 60, 30, 15, \dots

\newline

Note: the first term should be

a(1)

\newline

a(n)=\square

Determine First Term and Ratio: To find an explicit formula for a geometric sequence, we need to determine the first term $a(1)$ and the common ratio $r$ . The first term is given as $120$ .
Calculate Common Ratio: Next, we need to find the common ratio. The common ratio in a geometric sequence is found by dividing any term by the previous term. Let's divide the second term $60$ by the first term $120$ . $\newline$ $r = \frac{60}{120} = 0.5$
Write Explicit Formula: Now that we have the first term $a(1) = 120$ and the common ratio $r = 0.5$ , we can write the explicit formula for the $n$ th term of the geometric sequence as: $\newline$ $a(n) = a(1) \times r^{(n-1)}$
Substitute Values: Substituting the values of $a(1)$ and $r$ into the formula, we get: $\newline$ $a(n) = 120 \times (0.5)^{(n-1)}$ $\newline$ This is the explicit formula for the given geometric sequence.