Question

8) Solve the following recurrence relation with the given initial conditions:

?? = 10??−1 − 21??−2 ?0 = −3

?1 = 5

Answer 1

an -3,4, = 5 The given recurrence relation is = 10 an-,- 21 An-21 alo The characteristic equation of the above recurrence relation is 2 22 -10x +21 =D. 10+ 2 104.1.21 The roots are x = 2 10 I w 16 x 2 wi 10-4 x= 10+4 12 2 2 wy Hi = 3 dz = Thus the solution n an A 3^ + B Where A B are constants. D 0 av =- 3 =) A 3 TB. -3 =) A + B => 1 -3 1 21-5 >> A.3'+B. 7'= 5 => 13A + 7 B=5 solving and @ we get (2

3A+ 38 - - -१ 0x3: ex. 34 B = 5 -4B -14 ) B- 14 4 using the value of Bin o we get A + 14 4 = -3 =) A= -3 - 4 4 A = -२ 4 Hence the required solution is an 20 M 14 3 n +1 t 4 7 4