Write an equation for the $n$n th term of the geometric sequence. Then find $a_9$a9 .$1,\ 4,\ 16,\ 64,\ \ldots$1, 4, 16, 64, …$a_n=$an= $a_9=$a9=

Question

$1,\, 4,\, 16,\, 64,\, ext{...}$

$a_n=$

$a_9=$

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The general formula for the nth term of a geometric sequence is given by:

a_n = a_1 * r^(n-1)

where: a_n is the nth term a_1 is the first term r is the common ratio n is the term number

In this sequence, the first term a_1 is 1 and the common ratio r can be found by dividing the second term by the first term, which is 4/1 = 4.

So, the nth term of the sequence is given by:

a_n = 1 * 4^(n-1)

To find the 9th term a_9, we substitute n = 9 into the formula:

a_9 = 1 * 4^(9-1) = 1 * 4^8 = 65536

So, the 9th term of the sequence is 65536.

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