Question

Arithmetic Sequences Continued

Answer 1

Answer:

The common difference is 4

5, 9, 13, 17

Step-by-step 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