If $\{ a_{n}\}$ is a sequence with $a_{0} = p$ and $a_{n} - a_{n - 1} = ra_{n - 1}$ for $n \geq 1$, then the terms of the sequence are in

Question

Dr. Abubacker · Accepted Answer

(b)
Given, $a_{0} = p$ and $a_{n} - a_{n - 1} = ra_{n - 1}$
$\Rightarrow$ $a_{n} = a_{n - 1}(r + 1)$
For $n = 1$, $a_{1} = a_{0}(r + 1) = p(r + 1)$
$n = 2$, $a_{2} = a_{1}(r + 1) = p(r + 1)^{2}$
$n = 3$, $a_{3} = a_{2}(r + 1) = p(r + 1)^{3}$
This shows that the sequence is a geometric progression.

Q. If $\{ a_{n}\}$ is a sequence with $a_{0} = p$ and $a_{n} - a_{n - 1} = ra_{n - 1}$ for $n \geq 1$, then the terms of the sequence are in

Explanation

Reviewed by Dr. Abubacker

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