Find a formula for the nth term of the geometric sequence. Then find the indicated nth term of the geometric sequence.15th term: 4, 8, 16,. . .
Question
Find a formula for the nth term of the geometric sequence. Then find the indicated nth term of the geometric sequence.
15th term: 4, 8, 16, . . .
Solution
The 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 case, the first term a_1 is 4 and the common ratio r is 2 (since each term is twice the previous term).
So, the formula for the nth term of this sequence is:
a_n = 4 * 2^(n-1)
To find the 15th term, substitute n = 15 into the formula:
a_15 = 4 * 2^(15-1) a_15 = 4 * 2^14 a_15 = 4 * 16384 a_15 = 65536
So, the 15th term of the sequence is 65536.
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