Question

For each sequence, determine whether it appears to be geometric.
If it does, find the common ratio.
(a) 10, 30, 90, 270, ...
• Geometric
Common ratio:
r =
• Not geometric
(b) 10, 15, 20, 25, ...
• Geometric
Common ratio:
r =
• Not geometric
(c) 250, - 50, 10, - 2, ...
• Geometric
Common ratio:
• Not geometric

(No decimals)

Answer 1

To determine whether each sequence is geometric, we need to check if there is a constant ratio between consecutive terms. If a sequence is geometric, we can find the common ratio by dividing any term by the previous term.

(a) Sequence: 10, 30, 90, 270, ...
- Common ratio (r) = 30/10 = 3
- Common ratio (r) = 90/30 = 3
- Common ratio (r) = 270/90 = 3

Since the ratio is constant, the sequence is geometric.

• Geometric
Common ratio: r = 3

(b) Sequence: 10, 15, 20, 25, ...
- Common ratio (r) = 15/10 = 1.5
- Common ratio (r) = 20/15 = 1.333...
- Common ratio (r) = 25/20 = 1.25

The ratios are not constant, so the sequence is not geometric.

• Not geometric

(c) Sequence: 250, -50, 10, -2, ...
- Common ratio (r) = -50/250 = -0.2
- Common ratio (r) = 10/(-50) = -0.2
- Common ratio (r) = -2/10 = -0.2

Since the ratio is constant, the sequence is geometric.

• Geometric
Common ratio: r = -0.2

In summary:

(a) • Geometric, Common ratio: r = 3
(b) • Not geometric
(c) • Geometric, Common ratio: r = -0.2