Question

Given the explicit formula below, which is the appropriate list of the first 4 numbers:An = 3(2)n-1A2, 6, 18, 54, .B3, 6, 9, 12,..С3, 6, 12, 24, ...D1, 3, 5, 7, ...

Answer 1

The simpliest way to answer the question is by iteration, substituting n with the numbers 1, 2, 3, 4 to find the first 4 numbers. So we have the formula;

`A_n=3(2)^(n-1)`

When n = 1,

`\begin{gathered} A_n=3(2)^(n-1) \\ A_1=3(2)^(1-1) \\ A_1=3(2)^0 \\ A_1=3 \end{gathered}`

When n = 2,

`\begin{gathered} A_n=3(2)^(n-1) \\ A_2=3(2)^(2-1) \\ A_2=3(2)^1 \\ A_2=6^{} \end{gathered}`

When n = 3,

`\begin{gathered} A_n=3(2)^(n-1) \\ A_3=3(2)^(3-1) \\ A_3=3(2)^2 \\ A_3=12 \end{gathered}`

When n = 4,

`\begin{gathered} A_n=3(2)^(n-1) \\ A_4=3(2)^(4-1) \\ A_4=3(2)^3 \\ A_4=24 \end{gathered}`

Therefore when n = {1, 2, 3, 4}, An = {3, 6, 12, 24}, making 3, 6, 12, 24 the first 4 numbers of our formula.

Therefore the answer is LETTER C.