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

Given sequences :

–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, ….

Let us find the ratios.

–2, –4, –6, –8, –10,...

First sequence is just being decreased by -2. So it would be an Arithmetic sequence.

16, –8, 4, –2, 1 , ......

16/-8 = -2 and 4/-2 = -2.

In second sequence we got common ratio -2. Therefore, it's a geometric sequence.

–15, –18, –21.6, –25.92, –31.104, …

-15/-18 = 0.833

–21.6/ -18 = 0.833.

In second sequence we got common ratio 0.833. Therefore, it's a geometric sequence.

4, 10.5, 17, 23.5, 30, …

10.5/4 ≠ 17/10.5

Ratios are not same. So, it's not a geometric sequence.

625, 125, 25, 5, 1, ….

125/625 = 0.2 = 25/125.

In fourth sequence we got common ratio 0.2. Therefore, it's a geometric sequence.

Answer 2

The sequences which are geometric are;

• –8, 4, –2, 1

• -15, –18, –21.6, –25.92, –31.104

• 625, 125, 25, 5, 1,

A sequence is geometric if successive terms of the sequence differ by a given factor r.

In the question;

Geometric Sequence:

• –8, 4, –2, 1. has a common ratio,r = (-1/2)

• -15, –18, –21.6, –25.92, –31.104 has a common ratio, r = (1.2)

• 625, 125, 25, 5, 1 has a common ratio, r= (1/5)

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