A sequence ${{t}_{1}},{{t}_{2}},{{t}_{3}},{{t}_{4}},\ldots $ is given by \({{t}_{n+1}}=a+b{{t}_{n}

Question

A sequence ${{t}_{1}},{{t}_{2}},{{t}_{3}},{{t}_{4}},\ldots $ is given by ${{t}_{n+1}}=a+b{{t}_{n}}$, where $a$ and $b$ are non-zero constants. It is given that ${{t}_{3}}=320$, ${{t}_{4}}=240$ and ${{t}_{5}}=200$. Determine the value of $a$ and the value of $b$. Find the value of ${{t}_{6}}$. Show clearly that ${{t}_{1}}=800$. The sequence converges to a limit $L$. Determine the value of $L$.

Accepted Answer

(a) $a = 80$ $b = \frac{1}{2}$, (b) $t_6 = 180$ (c) $t_1 = 800$ (d) $L = 160$

T.Madas - Recurrence Relations Q37

T.Madas - Recurrence Relations Q37

Video Solution:

Solution:

Solution locked