Question

Which of the following sequences represents an arithmetic sequence with a common difference d = –5?

4, –20, 100, –500, 2,500
1,250, 250, 50, 10, 2
30, 25, 20, 15, 3
47, 42, 37, 32, 27

Answer 1

The answer is:

47, 42, 37, 32, 27

Work/explanation:

What is an arithmetic sequence?

An arithmetic sequence (or progression) is a sequence where we add/subtract the same amount, which is known as the common difference, to obtain the next number. So to solve this activity, we need to look for an arithmetic sequence, where we add -5 each time, or subtract 5 each time.

Option (a)

4, –20, 100, –500, 2,500

Clearly, we add way more than -5 here; not only do the numbers keep increasing fast, but we have a common ratio, not a common difference.

So this option is ruled out;

Option (b)

1,250, 250, 50, 10, 2

In this option, we divide by 5 each time; so this doesn't work either.

Option (c)

30, 25, 20, 15, 3

It looks like we're subtracting 5, but then the 3 throws us off; because to get from 15 to 3, you divide by 5.

Option (d)

47, 42, 37, 32, 27

Here, we add -5, or, in other words, we subtract 5.

Hence, the right choice is d.

Answer 2

The following arithmetic sequence represents a common difference of d = -5:

47, 42, 37, 32, 27

In an arithmetic sequence, values change through a common difference which adds or subtracts. In this sequence, each number decreases by 5 to receive an output of the next (47 - 5 = 42, 42 - 5 = 37, etc.).

None of the other sequences can be correct because they all eventually are solved with multiplication or division, which is an example of a geometric sequence. All options represent a sequence aside from option C, which both subtracts and divides by 5. Therefore, option D is the correct answer.