Question

Determine whether each sequence is geometric? 1) 60,48,36,24,12,… 2) 3,6,12,24,48,…

Answer 1

Answers:

1. Not geometric
2. Geometric

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Explanation for problem 1

Divide each term over its previous term.

• term2/term1 = 48/60 = 0.8
• term3/term2 = 36/48 = 0.75

We can stop here. The two results 0.8 and 0.75 do not match up, so we don't have a common ratio. Therefore, this sequence is not geometric. A geometric sequence must have each ratio of adjacent terms to be the same value throughout the list of numbers.

Side note: This sequence is arithmetic because we are subtracting the same amount each time (12) to generate each new term.

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Explanation for problem 2

Like before, we'll divide each term by its previous term.

• term2/term1 = 6/3 = 2
• term3/term2 = 12/6 = 2
• term4/term3 = 24/12 = 2
• term5/term4 = 48/24 = 2

Each ratio found was 2. This is the common ratio and it shows we have a geometric sequence. It indicates that each term is twice that of its previous term. Eg: the jump from 12 to 24 is "times 2".