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

We can find the first few terms of the sequence: $$14,14,14,14,\ldots$$ It's clear that the sequence is not decreasing, and it doesn't seem to be increasing either. One could also try to calculate more terms but this becomes time-consuming. However, since the initial two terms are the same, it's reasonable to guess that the limit of the sequence is also equal to $14$.

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

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