Question

Arithmetic Sequences Continued

A. Determine the common difference for each arithmetic sequence, then fill in the blanks.
5, _, _, 17

Answer 1

The common difference is 4

5, 9, 13, 17

Explanation:

Given

5, _, _, 17

Solving (a): The common difference

Since it is an arithmetic sequence, the common difference can be solved using:

`T_n = a + (n - 1)d`

Where

`a = 5`

`T_n = 17`

`n = 4` i.e. 4 terms

So:

`T_n = a + (n - 1)d`

`17 = 5 +(4 - 1) * d`

`17 = 5 +3d`

Collect like terms

`3d = 17 - 5`

`3d = 12`

`d =4`

Hence, the common difference is 4

Solving (b): Complete the blanks.

To do this, we simply add 4 to each successive terms.

So: 5, 9, 13, 17