$To find the first four terms of the sequence defined by the recurrence relation $ a_n = 4a_{n-1} $ with the initial condition $ a_1 = 4 $, we can calculate each term step-by-step: 1. $ a_1 = 4 $ 2. $ a_2 = 4a_1 = 4 \times 4 = 16 $ 3. $ a_3 = 4a_2 = 4 \times 16 = 64 $ 4. $ a_4 = 4a_3 = 4 \times 64 = 256 $ Thus, the first four terms of the sequence are $ 4, 16, 64, 256 $. The correct answer is **G. 4, 16, 64, 256**.$

First four terms of $a_n = 4a_{n-1}$ with $a_1 = 4$: 4, 16, 64, 256

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Question: A sequence can be generated by using an = 4a(n−1), where a1 = 4 and n is a whole number greater than 1. What are the first four terms in the sequence? F.4, 20, 100, 500 G.4,16, 64, 256 H.4, 8, 12, 16 J.4, 20, 40, 60

Asked by abdul1

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To generate the sequence using the given recurrence relation $a_n = 4a_{n-1}$, where $a_1 = 4$ and $n$ is a whole number greater than 1, we can follow these steps to determine the first four terms: 1. The first term $a_1$ is given as 4. 2. To find the second term $a_2$: \[ a_2 = 4a_1 = 4 \times 4 = 16 \] 3. To find the third term $a_3$: \[ a_3 = 4a_2 = 4 \times 16 = 64 \] 4. To find the fourth term $a_4$: \[ a_4 = 4a_3 = 4 \times 64 = 256 \] Thus, the first four terms in the sequence are: 4, 16, 64, 256. The correct answer is: G. 4, 16, 64, 256

Answered by gpt-4o

Feb. 4, 2025, 6:42 a.m.

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Published: Tuesday, February 4, 2025

First four terms of \(a_n = 4a_{n-1}\) with \(a_1 = 4\): 4, 16, 64, 256

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