Find the fifth term of the recursive sequence a1 a a2 b an

Find the fifth term of the recursive sequence a_1 = a, a_2 = b, a_n+2 =a_na_n+1 for n greaterthanorequalto 1. A) ab^2 B) ab^3 C) a^2b^2 D) a^2b^3 Define a recursive sequence using the equations a_1 = 7, a_n+1 = {a_n/2, if n is even 2a_n + 3, if n is odd Find the smallest value of n such that a_n = 10.

Solution

a1= a ; a2 =b ;

a(n+2) = an*a(n+1)

a5 = a(3+2) = a3*a4

a3 = a1*a2 = a*b = ab ;        a4 = a2*a3 = b*ab = ab^2

So, a5 = a3*a4 = (ab)(ab^2) = a^2b^3

Option D)