Question

21,42,126,504 If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose "not geometric.

Answer 1

Not geometric

Explanation:

In a geometric sequence, each term is multiplied by a common ratio to get the next term.

So if this is a geometric sequence, then dividing each term by the one before it should result in the same common ratio.

42 / 21 = 2

126 / 42 = 3

504 / 126 = 4

The ratios are different. This is not a geometric sequence.

Answer 2

Some tips for the future, when trying to find if its arithmetic or geometric sequence we can do this to find the common ratio. Arithmetic; subtraction test Geometric; division test

Ex; 19, 25, 31, 37

Subtract-

37-31= 6

31-25= 6

25-19= 6

6 is the common difference for this arithmetic sequence

Ex; 4, 8, 16, 32

Divide-

32/16= 2

16/8= 2

8/4= 2

The common ratio for the geometric sequence is 2

Explanation:

21, 42, 126, 504

504/126= 4

126/42= 3

42/21= 2

This is not a geometric sequence, there is no common ratio.