00:01
Hi, today we are solving the question in which recurrence relation is given by en is equals to 4an -1 plus 5en -2.
00:10
First two terms are given as e0 is 6 and e1 is equals to 18.
00:17
So first out of the five terms of the sequence defined by this recurrence relation is given by when n is equals to 0 so a0 is equals to 4 0 minus 1.
00:37
So if we take a1 for n is equals to 1.
00:42
So 1 4 a0 plus 5 a minus 2.
01:06
1 minus 2 will be minus 1 and similarly for a0 the relation will be 4 minus 1 a minus 1 plus 5 a minus minus 2.
01:35
So a2 is equals to 4 1 plus 4 a1 plus 5 a2.
02:02
5 a0.
02:03
A3 will be equal to 4 a2 plus 5 a1.
02:12
A4 is equals to 4 a3 plus 5 a2 and so on.
02:28
So if we substitute the values here so a0 will be given by the relation this itself.
02:41
So if we substitute a2 is equals to 4 into a1 that is 18 plus 5 into a0 it will be equal to 6.
02:52
So we get 72 plus 30.
03:00
We get 102.
03:01
Similarly for a3 we get 4 into 102 plus 5 into 18.
03:11
So we get 408 plus 90.
03:18
So 498 and for a4 we get it equals to 4 into 498 plus 5 into 102.
03:38
On solving it we get it as 1992 plus 510.
03:48
So it is equals to 2052...
