Step-by-step explanation:
Arithmetic sequence have a common difference so we need to find the common difference.
Formula for a arithmetic sequence is
[tex]y = a + (n - 1)d[/tex]
The 8th term is -32 and the third
term is -2
We need to find average rate of change so we just do
[tex] \frac{ - 32 - ( - 2)}{5} = \frac{ - 30}{5} = - 6[/tex]
So the average rate of change is -6 so we have
[tex]a +( - 6 )(n - 1) = [/tex]
We need to find the initial value, let just subtract -6 from -2 twice.
[tex] - 2 - ( - 6) - ( - 6) = 10[/tex]
So our inital value is 10
[tex]10 + ( - 6)(n - 1)[/tex]
