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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:

1. $0$
2. $1$
3. $2$
4. $-1$

### 1 comment

given that

h(m)=k, if m=0
= 1, if m=1
= 2h(m-1) + 4h(m-2), if m≥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

h(2)=2h(1)+4h(0) =2+4k
h(3)= 2h(2)+4h(1) = 4+8k+4 = 8+8k
h(4)= 2h(3)+4h(2) = 16+16k+8+16k= 32k+24 =88
32k=64
k=2
by
h(0)=k

h(1)=1

h(2)=2h(1)+4h(0)

=2+4k

h(3) =2h(2)+4h(1)

=4+8k+4 = 8+8k

Therefore, h(4)=32k+24 =88

Upon solving the recurrence we get

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