Question

WILL GIVE BRAINLIEST The sequence 7 21 63 189......shows the number of jumping jacks justin did each week, starting with the first week of him working out.

A. is the sequence arithmetic or geometric? how do you know?
B. What is the recursive rule for the sequence?
C. what is the iterative (explicit) rule for the sequence.

Answer 1

A

this is a geometric sequence since there exists a common ratio r between the terms

r = $\frac{21}{7}$ = $\frac{63}{21}$ = $\frac{189}{63}$ = 3

B

to obtain the next term in the sequence multiply the previous term by 3

$a_{n+1}$ = 3 $a_{n}$ ← recursive rule

C

the n th term of a geometric sequence is

$a_{n}$ = $a_{1}$ $r^{n-1}$

where $a_{1}$ is the first term in the sequence

$a_{n}$ = 7 × $3^{n-1}$ ← explicit rule