Write a recursive rule for the terms 2, 8, 32, 128

Question

Write a recursive rule, wrote an explicit rule in and find the 13th term

 

Answer 1

a₁=2¹   (=2)

a₂=2³   (=8)

a₃=2⁵   (=32)

....

a_n=2^2n-1

a_n=2²*a_2n-1  (this recurcive relation)

a₂/a₁=a₃/a₂=...=a_n/a_n-1=2² =q

 

a13=2^2*13-1=2²⁵= 33554432   [=2(4¹²)], coincides with Mark's answer.

 

Answer 2

a_n+1 = 4a_n

a_n = a₁(4)^n-1

a₁₃ = 2(4)¹²

 

Can you calculate?