If f ( 1 ) = 2 f(1)=2 and f ( n ) = 5 f ( n − 1 ) f(n)=5f(n−1) then find the value of f ( 5 )

Answer 1

This is a recursive formula so you can solve for each term using the previous term:

f(1) = 2

f(n) = 5f(n-1)

Solve for f(2) = 5f(1) = 10

then f(3)=5f(2) = 5(10) = 25,

f(4)=5f(3) = 5(25) = 125,

finally, f(5) = 5f(4) = 5(125) = 625.

Therefore, the value of f(5) = 625

Hope this helps!