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Solve the recurrence relation for the variables indicated below: bn = 8bn-1 - 15bn-2 b1 = 2 b2 = 16 If the explicit formula for the sequence is written in the form bn = u(s1)n + v(s2)n then find s1 and s2 .

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I'm not to sure but 36

The recurrence relation is given by bn = 8bn-1 - 15bn-2 with b1 = 2 and b2 = 16.

How to depict the solution?

Since it is linear homogeneous recurrence relation ,so first find its characteristic equation.

r² - 8r + 15 = 0

( r - 3 )( r - 5 ) = 0

r = 3 , 5

So, the general solution of the given recurrence relation is

bn = u(3)n + v(5)n ------------ ( 1 )

Now use the initial conditions b1 = 2 and b2 = 16.

From ( 1 ) , b1 = u(3)1 + v(5)1

2 = 3u + 5v ---------- ( 2 )

and b2 = u(3)2 + v(5)2

16 = 9u+ 25v------- ( 3 )

Solving ( 2 ) and ( 3 ) , we get u= - 1 and v = 1

Therefore, the required solution is bn = - (3)n + (5)n

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