Question

write a recursive formula for each sequence.

(a) write a recursive formula for \\(18,\\ 6,\\ -6,\\ -18,\\ \dots\\)
\\a_1 = \square\\
\\a_n = \square \text{ for } n \ge 2\\

(b) write a recursive formula for \\(10,\\ 40,\\ 160,\\ 640,\\ \dots\\)
\\a_1 = \square\\
\\a_n = \square \text{ for } n \ge 2\\

Explanation:

Analyze sequence (a)

$$
LATEXBLOCK0
$$

Analyze sequence (b)

$$
LATEXBLOCK1
$$

Answer:

Question 1

(a) Write a recursive formula for \(18, 6, -6, -18, \dots\)
\(a_1 =\) <blank>18</blank>
\(a_n =\) <blank>\(a_{n-1} - 12\)</blank> for \(n \ge 2\)

Question 2

(b) Write a recursive formula for \(10, 40, 160, 640, \dots\)
\(a_1 =\) <blank>10</blank>
\(a_n =\) <blank>\(4a_{n-1}\)</blank> for \(n \ge 2\)