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
Write an equation for the n th term of the geometric sequence. Then find a9 .1, 4, 16, 64, …an= a9=
Solution
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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