Write a recursive rule for the sequence.

Question

x+y, 3x+4y, 5x+7y, 7x+10y, …

Answer 1

A recursive sequence has a (1) base case of one or more elements, and a (2) recursive case for all other elements. The recursive case elements depend on previous elements to determine their value.

x+y

3x+4y

5x+7y

7x+10y

 . . .

The recursive definition is:

…

a₁ = x + y

a_n = a_n-1 + 2x + 3y       [ for n> 1

Answer 2

a_n+1x + b_n+1y = (a_n+2)x + (b_n+3)y where a₁=b₁=1