Determine whether the sequence is geometric. If so, then find the common ratio. 3, 12, 21, 30, . . .

Solution:

Given,

The sequence is 3, 12, 21, 30,...

We have to determine whether the sequence is geometric or not.

A geometric sequence is defined by its first term and common ratio ‘r’.

The common ratio is obtained by dividing the consecutive terms by each other.

A GP is of form a, ar, ar², ar³,.......arⁿ

From the given series,

Common ratio r = b/a = c/b = d/c

r = 12/3 = 21/12 = 30/21

12/3 = 4

21/12 = 1.75

30/21 = 1.43

r values are not constant.

The given sequence is an arithmetic sequence that has a common difference of 9.

Therefore, the given series is not a geometric series.

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Determine whether the sequence is geometric. If so, then find the common ratio. 3, 12, 21, 30, . . .

Summary:

The given sequence 3, 12, 21, 30,..is not geometric.