Question

How do you write the first five terms of the sequence defined recursively `a_1=32, a_(k+1)=1/2a_k`?

Answer 1

`a_1 = 32, a_2 = 16, a_3 = 8, a_4 = 4, a_5 = 2`

Explanation:

When `k=1, a_(k+1) = a_2 = 1/2 a_1 = 1/2(32) = 16`

When `k=2, a_(k+1) = a_3 = 1/2 a_2 = 1/2(16) = 8`

When `k=3, a_(k+1) = a_4 = 1/2 a_3 = 1/2(8) = 4`

When `k=4, a_(k+1) = a_5 = 1/2 a_4 = 1/2(4) = 2`

So: `a_1 = 32, a_2 = 16, a_3 = 8, a_4 = 4, a_5 = 2`