Answer:
[tex]a_4=-1271[/tex]
Step-by-step explanation:
We are given that:
[tex]a_1=10[/tex]
And:
[tex]a_{n+1}=-5a_n-1[/tex]
And we want to find:
[tex]a_4[/tex]
This is a recursive formula. So we can simply substitute in each value. For instance, a₂ will be:
[tex]a_2=a_{(1)+1}=-5a_{1}-1=-5(10)-1=-51[/tex]
Thus, a₃ will be:
[tex]a_3=a_{(2)+1}=-5a_2-1=-5(-51)-1=254[/tex]
Finally, a₄ will be:
[tex]a_4=a_{(3)+1}=-5a_3-1=-5(254)-1=-1271[/tex]
