Question

write a recursive formula for each sequence.
6, 12, 24, 48, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$
11, 5, -1, -7, ...
$a_1 = \square$
$a_n = \square$ for $n \geq 2$

Explanation:

Step1: Identify first term (Seq1)

$a_1 = 6$

Step2: Find recursive rule (Seq1)

$a_n = 2 \cdot a_{n-1}$ for $n \geq 2$

Step3: Identify first term (Seq2)

$a_1 = 11$

Step4: Find recursive rule (Seq2)

$a_n = a_{n-1} - 6$ for $n \geq 2$

Answer:

For sequence 6, 12, 24, 48, ...:
$a_1 = 6$
$a_n = 2a_{n-1}$ for $n \geq 2$

For sequence 11, 5, -1, -7, ...:
$a_1 = 11$
$a_n = a_{n-1} - 6$ for $n \geq 2$