Question

I need help to solve this!​

Answer 1

1. C. neither
2. B. exponential

Explanation:

You want to know the nature of the sequences ...

• 1, 4, 9, 16
• 1/3, 1, 3, 9, 27

Differences

To determine if a sequence is linear, you look at the differences between terms. If they are all the same, then the sequence is linear.

Here, the differences are ...

• 3, 5, 7
• 2/3, 2, 6, 18

Neither sequence is linear

Common factor

A sequence that is exponential will have adjacent terms with the same ratio.

Here, the ratios are ...

• 4/1, 9/4, 16/9
• 3, 3, 3, 3

The first sequence is not exponential. The second sequence is.

The sequences can be characterized as ...

1. neither
2. exponential

__

Additional comment

You may have noticed that the differences of the first sequence have a common difference of 2. This constant 2nd difference means the sequence can be described by a 2nd-degree (quadratic) polynomial. In fact, each term is the square of its term number.