The student who says that the sequence is not geometric is correct. See solution.
Practice makes perfect
We are given two consecutive terms of a sequence.
..., -8, 0, ...
If the sequence is a geometric sequence, then its nth term can be found by the formula below.
a_n=a_1(r)^(n-1)
Notice that one of the terms is 0, so we should be able to find it using the formula.
0=a_1(r)^(n-1)
By the Zero Product Property, a_1 or r should be 0. We have two cases.
If a_1= 0, then all terms have to be zero.
If r= 0, then all terms (with exception to the first term) have to be zero.
Note that - 8 is not the first term in the sequence, and it is not equal to zero. This means that the sequence is not a geometric sequence.
