Question

A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)?

Answer 1

Hey

Given, f( n + 1 ) = -10 f( n )

$= > \frac{f(n + 1)}{f(n)} = - 10$

$= > \prod^{n} _{1} \frac{f(k + 1)}{f(k)} = {( - 10)}^{n}$

$= > f(n + 1) = {( - 10)}^{n} f(1)$

$= > f(n) = {( - 10)}^{n - 1} f(1)$

Hence,

$f(3) = 100$