Question

Which sequence is geometric?

O1, 5, 9, 13,...
O2, 6, 8, 10,...
O 5, 7, 9, 11, ...
O4, 8, 16, 32,...

Answer 1

Geometric sequence:
`\sf \circ 4, 8, 16, 32, \ldots`

Explanation:

A sequence is geometric if each term after the first is found by multiplying the previous term by a fixed, nonzero number.

Let's check each sequence:

1.
`\sf 1, 5, 9, 13, \ldots`

• The common difference between consecutive terms is
  `\sf 4`, so this sequence is arithmetic, not geometric.

2.
`\sf 2, 6, 8, 10, \ldots`

• The common difference between consecutive terms is
  `\sf 4`, so this sequence is also arithmetic, not geometric.

3.
`\sf 5, 7, 9, 11, \ldots`

• The common difference between consecutive terms is
  `\sf 2`, so this sequence is arithmetic, not geometric.

4.
`\sf 4, 8, 16, 32, \ldots`

• The common ratio between consecutive terms is
  `\sf 2`, so this sequence is geometric.

Therefore, the sequence
`\sf 4, 8, 16, 32, \ldots` is the geometric sequence among the given options.

Answer 2

The sequence that is geometric is 4, 8, 16, 32,... In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 2 (8/4 = 2, 16/8 = 2, 32/16 = 2).