Find all solution of the recurrences relation an-8an-1+16an-2=0with initial condition a2=16,a3=80
Answers
=a+d=16-------->1
a3
= a+2d=80----> 2
Now, (-)
a + d = 16
a +2d= 80
(-) (-) (-)
---------------
-d = -64
d = 64
Now substitute d = 64 in 1 , we get
a = 16 - d
a = 16 - 64
a = -48
Given that,
an - 8an -1 + 16an -2 = 0
16an + an - 8an - 1 - 2 = 0
17an - 8an - 3 = 0
9an = 3
an = 3/9
an = 1/3
Given:
an- 8an- 1+ 16an- 2= 0 with initial condition
a2 = 16, a3 = 80
To Find:
the recurrences value
Solution:
a2 = a + d = 16...[1]
a3 = a + 2d =180 ..[2]
Now,
using [1] and [2] a + d = 16
a + 2d = 80
after subtracting value of -d = -64
d = 64
now, substituting d = 64 in [1]
a2 = a+ d = 16
a2 = a + 16 = 16
a = -48
Given that,
an - 8an - 1 + 16an - 2 = 0
16an + an - 8an - 1 - 2 =0
17an - 8an - 3 = 0
9an = 3
an = 9/3
an = 1/3
Therefore, the recurrence relation an=1/3.