81,41,21,...The 14th term in this geometric sequence is 1024.
The nth term in this sequence is given by the formula:
Explicit Formula: an=2n−4
Recursive Formula: an=2an−1,where a1=81
81×241×221
Explicit Formula
The formula for a geometric sequence where a1 is the 1st term, r is the common ratio, and n is the term number is an=a1rn−1
Find a1 and r: a1r=81=2
The nth term rule is:an=a1rn−1=81(2)n−1=2n−4
Recursive Formula
The formula for a geometric sequence where an−1 is the (n-1)th term, r is the common ratio, and n>1 is an=ran−1
Find r: r=2
The nth term rule is:an=ran−1=(2)an−1=2an−1