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

Feb 24, 2017

${a}_{1} = 32 , {a}_{2} = 16 , {a}_{3} = 8 , {a}_{4} = 4 , {a}_{5} = 2$

#### Explanation:

When $k = 1 , {a}_{k + 1} = {a}_{2} = \frac{1}{2} {a}_{1} = \frac{1}{2} \left(32\right) = 16$

When $k = 2 , {a}_{k + 1} = {a}_{3} = \frac{1}{2} {a}_{2} = \frac{1}{2} \left(16\right) = 8$

When $k = 3 , {a}_{k + 1} = {a}_{4} = \frac{1}{2} {a}_{3} = \frac{1}{2} \left(8\right) = 4$

When $k = 4 , {a}_{k + 1} = {a}_{5} = \frac{1}{2} {a}_{4} = \frac{1}{2} \left(4\right) = 2$

So: ${a}_{1} = 32 , {a}_{2} = 16 , {a}_{3} = 8 , {a}_{4} = 4 , {a}_{5} = 2$