Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
-$4,16,64,256 , \ldots$
A) $a _ { n } = \mathrm { n } + 2$
B) $a _ { n } = 2 ^ { n - 1 }$
C) $a _ { n } = 2 ^ { n }$
D) $a _ { n } = 2 n$

Question

Quizplus · Accepted Answer

Each term in the sequence is obtained by multiplying the previous term by 4, which can be represented as $2^2$. The first term is $4 = 2^2$, the second term is $16 = 2^4$, the third term is $64 = 2^6$, and the fourth term is $256 = 2^8$. This pattern suggests that the nth term is $2^{2n}$, but since the sequence starts with $2^2$ as the first term, the formula needs to account for this initial offset. The correct formula that fits the sequence is $a_n = 2^{2n}$, but none of the provided options exactly match this. However, option C, $a_n = 2^n$, is the closest in form, suggesting a misunderstanding in the explanation. The correct explanation is that each term is 4 times the previous one, starting with 4, and the sequence actually follows a geometric progression with the common ratio of 4, not $2^n$. My initial explanation was incorrect; the sequence is indeed a geometric progression, but the correct formula for its nth term is not provided in the options. The sequence is $4, 16, 64, 256, \ldots$, which is $2^2, 2^4, 2^6, 2^8, \ldots$, indicating each term is $2^{2n}$, not $2^n$ as previously stated.

Find the Nth Term ana _ { n }an​ Of a Sequence Whose First Four Terms Are Given

Find the Nth Term $a _ { n }$ Of a Sequence Whose First Four Terms Are Given