Geometric Sequence Warmup 3

What is the common ratio for the sequence:
28, 14, 7, 3.5...

• 2

• 1/2

• -14

• -7

Answer explanation

To find the common ratio, divide each term by the previous one. For example, 14/28 = 1/2, 7/14 = 1/2, and 3.5/7 = 1/2. Thus, the common ratio is 1/2.

Tags

CCSS.HSF.BF.A.2

Find the next three terms: 4, 12, 36, 108, ...

• 324, 972, 2916

• 972, 2916, 8748

• 405, 1215, 3645

Answer explanation

The pattern is multiplying by 3: 4x3=12, 12x3=36, 36x3=108. Continuing, 108x3=324, 324x3=972, 972x3=2916. Thus, the next three terms are 324, 972, 2916.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

Is the sequence -432, 72, -12, 2,...geometric?

• yes

• no

Answer explanation

The sequence is geometric because each term is obtained by multiplying the previous term by a constant ratio. The ratio is -1/6, as -432 * (-1/6) = 72, 72 * (-1/6) = -12, and -12 * (-1/6) = 2. Thus, the answer is yes.

Determine whether the sequence is arithmetic, geometric, or neither.

• arithmetic

• geometric

• neither

Answer explanation

The sequence is geometric because each term is obtained by multiplying the previous term by a constant ratio. In contrast, an arithmetic sequence adds a constant difference between terms.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

Is the sequence 2, 4, 12, 48,... geometric?

• yes

• no

Answer explanation

The sequence is not geometric because the ratio between consecutive terms is not constant. For example, 4/2 = 2, but 12/4 = 3 and 48/12 = 4. Since the ratios differ, the answer is no.

Tags

CCSS.HSF.BF.A.2