Is the following a geometric sequence 1, -2, 4, -8, 16,…?

1 Answer
Nov 25, 2015

Answer:

The terms listed are consistent with being a geometric sequence with initial term #1# and common ratio #-2#

Explanation:

The ratio of any two successive terms listed is #-2#, so this can be a geometric sequence. I say can be because we do not know what the following terms are.

For example, the same terms are given by the formula:

#a_n = 1/(0!)-3/(1!)(n-1)+9/(2!)(n-1)(n-2)#

#-27/(3!)(n-1)(n-2)(n-3)+81/(4!)(n-1)(n-2)(n-3)(n-4)#

but this formula would make #a_6 = 211# rather than #-32#