How do you find the explicit formula for: 1, 2, 4, 8...?

1 Answer
Alan P.
Feb 18, 2016

a_n = 2^(n-1)

Explanation:

The difference between successive terms is not a constant,
so the sequence is not an arithmetic sequence.

Checking to see if the sequence might be geometric,
we see the successive terms are all a multiple of 2 times the previous term.

a_1=1=2^0
a_2=a_1xx2=2^1
a_3=a_2xx2=a_1xx2^2 = 2^2
a_4=a_3xx2=a_1xx2^3=2^3

so we could generalize:
color(white)("XXX")a_n=2^(n-1)

Related questions
See all questions in Geometric Sequences
Impact of this question
12380 views around the world
You can reuse this answer
Creative Commons License