High School Pre-Cal

Question

What is the 7th term of the recursive sequence below?

 

a₁=2

a₂=-1

a_n=(a_n-1)(a_n-2)



A.32

B.2

C.–128

D.–256

Answer 1

first term is A1 = 2

 

second term is A2 = -1

 

A3 = A2*a1 = (2)(-1) = -2

 

A4 = a3*a2 = (-2)(-1) = 2

 

a5 = a4*a3 = (2)(-2) = -4

 

a6 = a5*a4 = (-4)(2) = -8

 

a7 = a6*a5 = (-8)(-4) = 32 <--- 7th term

 

a8 = a7*a6 = (32)(-8) = -256 <--- 8th term

 

a9 = a8*a7 = (-256)(32) = -8192

 

A