Question

He first term of a sequence is 2, and each subsequent term is the reciprocal of the square of the preceding term. what is the positive square root of the fifth term?

Answer 1

The first term is a₁ = 2.
Each subsequent term is the reciprocal of the square of the preceding term.

2nd term:
a₂ = 1/2² = 1/4

3rd term:
a₃ = 1/(1/4)² = 1/(1/16) = 16

4th term:
a₄ = 1/16² = 1/256

5th term:
a₅ = 1/(1/256)² = 1/(1/65536) = 65536
The positive square root of the fifth term is
√(65536) = 256

Answer: 256