Write out the first 4 terms of the following sequence that is define recursively.
a1=32
ak+1=1/2ak
well, just plug and chug
a1 = 32
a2 = 1/2 (32) = 16
a3 = 1/2 (16) = 8
...
To find the first 4 terms of a sequence defined recursively, we will use the given recursive formula. Let's break it down step by step.
The given recursive formula is:
a1 = 32
ak+1 = 1/2ak
To find the second term (a2), we substitute k = 1 into the recursive formula:
a2 = 1/2a1
= 1/2 * 32
= 16
To find the third term (a3), we substitute k = 2 into the recursive formula:
a3 = 1/2a2
= 1/2 * 16
= 8
To find the fourth term (a4), we substitute k = 3 into the recursive formula:
a4 = 1/2a3
= 1/2 * 8
= 4
Therefore, the first four terms of the sequence defined recursively are: 32, 16, 8, 4.