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

1 Answer
Feb 18, 2016

Answer:

#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)#