Math, asked by 1adildaa, 1 month ago

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).

Answers

Answered by senboni123456
0

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}

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