What will be the 7th term of the geometric sequence 1, 4, 16, ...?*1 pointA. 1024B. 4096C. 16384D. 32768
Question
What will be the 7th term of the geometric sequence 1, 4, 16, ...?
1 point
A. 1024
B. 4096
C. 16384
D. 32768
Solution
The 7th term of a geometric sequence can be found using the formula:
a_n = a_1 * r^(n-1)
where: a_n is the nth term we're looking for, a_1 is the first term in the sequence, r is the common ratio, and n is the position of the term.
In this case, a_1 is 1, r is 4 (since each term is 4 times the previous term), and n is 7.
So, the 7th term is:
a_7 = 1 * 4^(7-1) = 1 * 4^6 = 1 * 4096 = 4096
So, the 7th term of the sequence is 4096. Therefore, the correct answer is B. 4096.
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