Question

Which sequences are geometric? Check all that apply.

–2, –4, –6, –8, –10, …
16, –8, 4, –2, 1
–15, –18, –21.6, –25.92, –31.104, …
4, 10.5, 17, 23.5, 30, …
625, 125, 25, 5, 1, …

Answer 1

A geometric sequence has a constant ratio r = (next term)/(current term).

Check each:

- –2, –4, –6, –8, –10, …: ratios are (−4)/(−2)=2, (−6)/(−4)=1.5 → not constant, so NOT geometric.
- 16, –8, 4, –2, 1: ratios = (−8)/16 = −1/2, 4/(−8)=−1/2, … constant r = −1/2 → geometric.
- −15, −18, −21.6, −25.92, −31.104, …: ratios = (−18)/(−15)=1.2, (−21.6)/(−18)=1.2, … constant r = 1.2 (6/5) → geometric.
- 4, 10.5, 17, 23.5, 30, …: ratios = 10.5/4 = 2.625, 17/10.5 ≈ 1.619… → not constant, so NOT geometric.
- 625, 125, 25, 5, 1, …: ratios = 125/625 = 1/5, 25/125 = 1/5, … constant r = 1/5 → geometric.

So the geometric sequences are: 16, −8, 4, −2, 1; −15, −18, …; and 625, 125, 25, 5, 1.