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:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 5[/tex]
[tex]T_n = 17[/tex]
[tex]n = 4[/tex] i.e. 4 terms
So:
[tex]T_n = a + (n - 1)d[/tex]
[tex]17 = 5 +(4 - 1) * d[/tex]
[tex]17 = 5 +3d[/tex]
Collect like terms
[tex]3d = 17 - 5[/tex]
[tex]3d = 12[/tex]
[tex]d =4[/tex]
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
