A recursive function $h$, is defined as follows:

$\begin{array} {} h(m) & =k, \text{if } m=0 \\ &=1, \text{if } m=1 \\ &= 2 h(m-1)+4h(m-2), \text{if } m \geq 2 \end{array}$

If the value of $h(4)$ is $88$ then the value of $k$ is:

https://gateoverflow.in/113801/ugcnet-dec2016-iii-24

given that

h(m)=k, if m=0 = 1, if m=1 = 2h(m-1) + 4h(m-2), if mâ‰¥2 If the value of h(4) is 88 then the value of k is

h(4)=2h(3)+4h(2)=2(2h(2)+4h(1))+4h(2) =8h(2)+8h(1)=8(2h(1)+4h(0))+8h(1)=24h(1)+32h(0)=24+32k=88=>k=2

hence ans is option 3

Upon solving the recurrence we get