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Consider a sequence $F_{00}$ defined as :

$F_{00}\left ( 0 \right )= 1, F_{00}\left ( 1 \right )= 1\\$

$F_{00}\left ( n \right )= \frac{10 * F_{00}\left ( n-1 \right )+100}{F_{00}\left ( n-2 \right )} \text{ for }n\geq 2 \\$

Then what shall be the set of values of the sequence $F_{00}$ ?

1. $\left ( 1,110,1200 \right )$
2. $\left ( 1,110, 600,1200 \right )$
3. $\left ( 1, 2, 55, 110, 600, 1200 \right )$
4. $\left ( 1, 55, 110, 600, 1200 \right )$

F00(2)= (10*F00(1)+100)/F00(0) = (10*1 +100)/1=110

F00(3)=10* F00(2)+100)/F00(1)=(10*110 + 100)/1 = 1200
so, Option 1

Ans is A

GIVEN

$F_{00} (0) = 1$,

$F_{00} (1) = 1$,

$F_{00}(n) = ((10 *F (n − 1) + 100)/F00 (n − 2)) for n \geqslant2$

Let n=2
$F_{00} (2) = (10 * F_{00} (1) + 100)/F_{00} (2-2)$
=$(10 * 1 + 100)/1$
= $(10 + 100)/1$
=$110$

Let n=3
$F_{00} (3) = (10 * F_{00} (2) + 100)/F_{00} (3 - 2)$
= $(10 * 110 + 100)/1$
= $(1100 + 100)/1$
= $1200$

Similarly, n=4
$F_{ 00} (4) = (10 * F_{00} (3) + 100) /F_{00} (4- 2)$

=$10*1200+100/110$
= $(12100)/110$
=$110$

Similarly, n=5

$F 00 (5) = (10 * F00 (4) +100) /F00(5-2)$
= $(10*110 + 100) / 1200$
= $1200/1200$

=$1$

The sequence will be $(1, 110, 1200,110,1)$

0ption A

1
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