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Find an explicit formula for the geometric sequence

3,15,75,375,....". "
Note: the first term should be a(1).

a(n)=

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

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Experimental probability

Full solution

Q. Find an explicit formula for the geometric sequence

\newline

3

,

15

,

75

,

375

, .......

\newline

Note: the first term should be

a(1)

.

\newline

a(n)=

Calculate Common Ratio: We need to identify the common ratio $r$ of the geometric sequence. To do this, we divide the second term by the first term. $\newline$ Calculation: $r = \frac{15}{3} = 5$
Write Explicit Formula: Now that we have the common ratio, we can write the explicit formula for the $n$ th term of a geometric sequence, which is $a(n) = a(1) \times r^{(n-1)}$ , where $a(1)$ is the first term and $r$ is the common ratio.
Plug in Values: We know the first term $a(1)$ is $3$ and the common ratio $r$ is $5$ . Plugging these values into the formula gives us the explicit formula for the sequence. $\newline$ Calculation: $a(n) = 3 \times 5^{(n-1)}$

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