Consider the sequence built by the following rule: $A _ { 1 } = 1 , A _ { 2 } = 3 , A _ { n + 1 } = A _ { n } + 2 \cdot A _ { n - 1 } \text { for } n \geq 2$ What is $A _ { 4 } ?$
A) 6
B) 10
C) 11
D) 15

Question

Quizplus · Accepted Answer

We can find each term of the sequence by using the given recursive rule.

\begin{align*}
A_3 &= A_2 + 2A_1 = 3 + 2(1) = 5 \
A_4 &= A_3 + 2A_2 = 5 + 2(3) = 11
\end{align*}

Therefore, the answer is C, 11.

Consider the Sequence Built by the Following Rule A1=1,A2=3,An+1=An+2⋅An−1 for n≥2A _ { 1 } = 1 , A _ { 2 } = 3 , A _ { n + 1 } = A _ { n } + 2 \cdot A _ { n - 1 } \text { for } n \geq 2A1​=1,A2​=3,An+1​=An​+2⋅An−1​ for n≥2

Consider the Sequence Built by the Following Rule $A _ { 1 } = 1 , A _ { 2 } = 3 , A _ { n + 1 } = A _ { n } + 2 \cdot A _ { n - 1 } \text { for } n \geq 2$