Question #137266
The recursive definition of a function X is given as:
f(0)=5 and f(n)=f(n-2)+5
Now, find out the value of f(14) using the above function.
1
Expert's answer
2020-10-07T19:02:54-0400

Given:f(0)=5  and  f(n)=f(n2)+5To  find:  f(14)\mathbf{Given : f(0)=5\;and\;f(n)=f(n-2)+5}\\ \\ \\ \\ \\ \mathbf{To\;find:\;f(14)}


Put  n=14  in  the  recursive  definition  of  function\mathbf{Put\;n=14\;in\;the\;recursive\;definition\;of\;function}

we  get\mathbf{we \;get-}


f(14)=f(142)+5=f(12)+5    f(14)=(f(122)+5)+5=f(10)+10    f(14)=(f(102)+5)+10=f(8)+15    f(14)=(f(82)+5)+15=f(6)+20    f(14)=(f(62)+5)+20=f(4)+25    f(14)=(f(42)+5)+25=f(2)+30    f(14)=(f(22)+5)+30=f(0)+35    f(14)=5+35=40    (  f(0)=5)f(14)=40\mathbf{\therefore f(14)=f(14-2)+5=f(12)+5}\\ \\ \mathbf{\implies f(14)=(f(12-2)+5)+5=f(10)+10}\\ \\ \mathbf{\implies f(14)=(f(10-2)+5)+10=f(8)+15}\\ \\ \mathbf{\implies f(14)=(f(8-2)+5)+15=f(6)+20}\\ \\ \mathbf{\implies f(14)=(f(6-2)+5)+20=f(4)+25}\\ \\ \mathbf{\implies f(14)=(f(4-2)+5)+25=f(2)+30}\\ \\ \mathbf{\implies f(14)=(f(2-2)+5)+30=f(0)+35}\\ \\ \mathbf{\implies f(14)=5+35=40\;\;(\because\; f(0)=5)}\\ \\ \mathbf{\therefore f(14)=40}












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Comments

Assignment Expert
08.10.20, 17:56

Dear Chowdhury Sidhratul Montaha, please use the panel for submitting new questions.

Assignment Expert
08.10.20, 17:55

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Chowdhury Sidhratul Montaha
08.10.20, 12:38

“Measurement of time intervals are affected by relative motion between an observer if you agree with the statement, explain the above statement.

Raziya Sultana
08.10.20, 06:41

Thank you for your answer.

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