Question

Read the first few terms of a sequence below. Then, identify the type of sequence that this is an example of:

"1, 4, 6, 16, 34, ..."

Answer 1

The given sequence is an example of a quadratic sequence.

Step-by-step explanation:

The given sequence "1, 4, 6, 16, 34, ..." is an example of a quadratic sequence. In a quadratic sequence, the difference between consecutive terms is not constant. Instead, the difference between consecutive terms forms its own sequence. In this case, the differences between consecutive terms are: 3, 2, 10, 18, ...

To determine the pattern in the differences, we can calculate the differences between consecutive differences. The differences between the differences are: -1, 8, 8, ...

Since the differences between the differences are constant, we can conclude that the sequence follows a quadratic pattern.