Consider the real valued function h: 0,1,2 ldots ldots ldots 100 arrow R such that h(0)=5, h(100)=20 and satisfying h(p)=(1/2) h(p+1)+h(p-1) for every p=1,2 ldots ldots .99. Then the value of h(1) is

Question

Consider the real valued function h: 0,1,2 ldots ldots ldots 100 arrow R such that h(0)=5, h(100)=20 and satisfying h(p)=(1/2) h(p+1)+h(p-1) for every p=1,2 ldots ldots .99. Then the value of h(1) is (A) 5.15 (B) 5.5 (C) 6 (D) 6.15

Tardigrade Admin · Accepted Answer

h(p)=(1/2)(h(p+1)+h(p-1)) ⇒ h(p-1), h(p), h(p+1) are in A.P. h(100)=h(0)+99 d ⇒ (20-5/99)=d ⇒ d=(15/99) ⇒ h(1)=h(0)+d =5+(15/99)=5.15

Q. Consider the real valued function $h : {0, 1, 2 \dots\dots\dots 100} \to R$ such that $h (0) = 5, h (100) = 20$ and satisfying $h (p) = \frac{1}{2} {h (p + 1) + h (p - 1)}$ for every $p = 1, 2 \dots\dots .99$ . Then the value of $h (1)$ is

5.15

5.5

6

6.15

$h (p) = \frac{1}{2} (h (p + 1) + h (p - 1))$
$\Rightarrow h (p - 1), h (p), h (p + 1)$ are in A.P.
$h (100) = h (0) + 99 d$
$\Rightarrow \frac{20 - 5}{99} = d$
$\Rightarrow d = \frac{15}{99}$
$\Rightarrow h (1) = h (0) + d$
$= 5 + \frac{15}{99} = 5.15$

Q. Consider the real valued function h:{0,1,2………100}→R such that h(0)=5,h(100)=20 and satisfying h(p)=21​{h(p+1)+h(p−1)} for every p=1,2…….99. Then the value of h(1) is

5.15

5.5

6

6.15

h(p)=21​(h(p+1)+h(p−1)) ⇒h(p−1),h(p),h(p+1) are in A.P. h(100)=h(0)+99d ⇒9920−5​=d ⇒d=9915​ ⇒h(1)=h(0)+d =5+9915​=5.15

Q. Consider the real valued function $h : {0, 1, 2 \dots\dots\dots 100} \to R$ such that $h (0) = 5, h (100) = 20$ and satisfying $h (p) = \frac{1}{2} {h (p + 1) + h (p - 1)}$ for every $p = 1, 2 \dots\dots .99$ . Then the value of $h (1)$ is

$h (p) = \frac{1}{2} (h (p + 1) + h (p - 1))$
$\Rightarrow h (p - 1), h (p), h (p + 1)$ are in A.P.
$h (100) = h (0) + 99 d$
$\Rightarrow \frac{20 - 5}{99} = d$
$\Rightarrow d = \frac{15}{99}$
$\Rightarrow h (1) = h (0) + d$
$= 5 + \frac{15}{99} = 5.15$