Question

What is the common difference between the elements of the arithmetic sequence below?

–18, –22.5, –27, –31.5, –36

Answer 1

In an arithmetic sequence, the difference between consecutive terms is constant and is referred to as the common difference. To find the common difference, we will subtract the first term from the second term.

Let's denote the terms of the sequence as follows:
- \( a_1 = -18 \)
- \( a_2 = -22.5 \)
- \( a_3 = -27 \)
- \( a_4 = -31.5 \)
- \( a_5 = -36 \)

The common difference (\(d\)) can be found by using the formula:
\[ d = a_2 - a_1 \]

Let's calculate it:
\[ d = -22.5 - (-18) \]
\[ d = -22.5 + 18 \]
\[ d = -4.5 \]

To confirm the common difference, calculate it between other consecutive terms:
For \( a_3 - a_2 \):
\[ d = -27 - (-22.5) \]
\[ d = -27 + 22.5 \]
\[ d = -4.5 \]

For \( a_4 - a_3 \):
\[ d = -31.5 - (-27) \]
\[ d = -31.5 + 27 \]
\[ d = -4.5 \]

For \( a_5 - a_4 \):
\[ d = -36 - (-31.5) \]
\[ d = -36 + 31.5 \]
\[ d = -4.5 \]

Thus, the common difference between the elements of the arithmetic sequence is \(-4.5\).