Question

Let f be a function defined by f(n) = 2f(n-1) +3f(n-2), where f(1) = 1 and f(2) = 2. Determine f(5).

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{f(n)=2\,f(n-1)+3\,f(n-2)}$

Given, f(1)=1 and f(2)=2

Put n = 3 in the above functional equation

$\sf{f(3)=2\,f(3-1)+3\,f(3-2)}$

$\sf{\implies\,f(3)=2\,f(2)+3\,f(1)}$

$\sf{\implies\,f(3)=2\times2+3\times1}$

$\sf{\implies\,f(3)=7}$

Put n = 4

$\sf{f(4)=2\,f(4-1)+3\,f(4-2)}$

$\sf{\implies\.f(4)=2\,f(3)+3\,f(2)}$

$\sf{\implies\.f(4)=2\times7+3\times2}$

$\sf{\implies\.f(4)=20}$

Put n = 5

$\sf{f(5)=2\,f(5-1)+3\,f(5-2)}$

$\sf{\implies\,f(5)=2\,f(4)+3\,f(3)}$

$\sf{\implies\,f(5)=2\times20+3\times7}$

$\sf{\implies\,f(5)=61}$