Answer:
[tex]A(n) = -4n -10[/tex]
Step-by-step explanation:
Given
[tex]Sequence:\ -10, -14, -18, -22[/tex]
Required
Determine the formula for the nth term
The sequence shows arithmetic progression.
So, we need to determine the common difference (d) first
[tex]d = A_2 - A_1[/tex]
In this case:
[tex]A_2 = 2nd\ Term = -14[/tex]
[tex]A_1 = 1st\ Term = -10[/tex]
So:
[tex]d = -14 - (-10)[/tex]
[tex]d = -14 + 10[/tex]
[tex]d = -4[/tex]
The nth term is then calculated as thus:
[tex]A(n) = A_1 + (n - 1)d[/tex]
[tex]A(n) = -14 + (n - 1)* -4[/tex]
[tex]A(n) = -14 -4n + 4[/tex]
[tex]A(n) = -4n + 4-14[/tex]
[tex]A(n) = -4n -10[/tex]
