A sequenceis $\left\{ a _ { n } \right\}$ defined recursively by the equation $a _ { n } = 0.5 \left( a _ { n - 1 } + a _ { n - 2 } \right)$ for $n \geq 3$ where $a _ { 1 } = 14 , a _ { 2 } = 14$. Use your calculator to guess the limit of the sequence.
A) 6
B) 14
C) 26
D) 17
E) 15

Question

Quizplus · Accepted Answer

As the value of $n$ increases, $a_n$ is calculated as the average of the two previous terms $a_{n-1}$ and $a_{n-2}$. Since the initial terms are both $14$, the sequence will converge to the value $\boxed{14}$.

A Sequenceis {an}\left\{ a _ { n } \right\}{an​} Defined Recursively by the Equation

A Sequenceis $\left\{ a _ { n } \right\}$ Defined Recursively by the Equation