Question

Study the sequences (0, 6, 12, 18, 24, . . .) and (1, 6, 36, 216, 1,296, . . .), and answer these questions:

Which of the two sequences is an arithmetic sequence?
What is the common difference of the arithmetic sequence?
Can you think of any other mathematical relationship that exhibits a common difference between numbers?

Answer 1

Answer: In the first sequence, subtracting the previous term from each term starting from the second one gives these values:

6 – 0 = 6, 12 – 6 = 6, 18 – 12 = 6, and 24 – 18 = 6.

The difference of the terms is constant. This sequence is an arithmetic one, with the common difference being 6.

Just by looking at the terms in the second sequence, (1, 6, 36, 216, 1,296, . . .), it’s clear that the difference of the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.

Like arithmetic sequences, linear equations show a common difference between numbers.

Step-by-step explanation: Edmentum Answer

Answer 2

Explanation:

In the first sequence, subtracting the previous term from each term starting from the second one gives these values: (0, 6, 12, 18, 24, . . .) is an arithmetic sequence.

How to find the common difference in the arithmetic sequence?

Common difference = second term - first term

The difference between the terms is constant. This sequence is an arithmetic one, with the common difference being 6.

Common difference = 6.

Just by looking at the terms in the second sequence,

(1, 6, 36, 216, 1,296, . . .), the difference between the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.

Like arithmetic sequences, linear equations show a common difference between numbers.