Question

What is the fourth term of the sequence defined by a1 3xy 5 an (___2x y )an 1? (1) 12x 3 y 3 (3) 24x 4 y 2 (2) 24x 2 y 4 (4) 48x 5 y 1?

Answer 1

a1=3xy^ 5

an= (2x/ y )a(n-1)

then

a2=(2x/ y )a(1)= (2x/ y )* 3xy^ 5=6(x^ 2)(y^ 4)

a2=6(x^ 2)(y^ 4)

a3=(2x/ y )a(2)= (2x/ y )* 6(x^ 2)(y^ 4)=12(x^ 3)(y^ 3)

a3=12(x^ 3)(y^ 3)

a4=(2x/ y )a(3)=(2x/ y )*12(x^ 3)(y^ 3)=24(x^ 4)(y^ 2)

 The answer is a4=24(x^ 4)(y^ 2)