Question

write a recursive formula for each sequence.
32, 16, 8, 4, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$
2, 8, 32, 128, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term (Seq1)

$a_1 = 32$

Step2: Find recursive rule (Seq1)

Each term is $\frac{1}{2}$ prior term: $a_n = \frac{1}{2}a_{n-1}$ for $n\geq2$

Step3: Identify first term (Seq2)

$a_1 = 2$

Step4: Find recursive rule (Seq2)

Each term is 4× prior term: $a_n = 4a_{n-1}$ for $n\geq2$

Answer:

For sequence 32, 16, 8, 4, ...:
$a_1 = 32$
$a_n = \frac{1}{2}a_{n-1}$ for $n \geq 2$

For sequence 2, 8, 32, 128, ...:
$a_1 = 2$
$a_n = 4a_{n-1}$ for $n \geq 2$