Hello, pwr_hngry!

The characteristic equation is: .r² - 7r + 10 .= .0Solve the given recurrence relation with for the initial conditions given.

an .= .7an-1 - 10an-2, .a0 = 5, .a1 = 16

. . which factors: .(r - 2)(r - 5) .= .0

. . and has roots: .r .= .2, 5

So we have: .an .= .b·2^n + c·5^n

From a0 = 5, we have: .b·2^0 + c·5^0 .= .5 . . → . . b + c .= .5

From a1 = 16, we have: .b·2^1 + c·5^1 .= .16 . . → . . 2b + 5c .= .16

Solve the system of equations and get: .b = 3, .c = 2

Therefore: .an .= .3·2^n + 2·5^n