Question

If a1=10 and an+1=-5an-1 then find the value of a4

Please explain!

Answer 1

`a_4=-1271`

Explanation:

We are given that:

`a_1=10`

And:

`a_(n+1)=-5a_n-1`

And we want to find:

`a_4`

This is a recursive formula. So we can simply substitute in each value. For instance, a₂ will be:

`a_2=a_((1)+1)=-5a_(1)-1=-5(10)-1=-51`

Thus, a₃ will be:

`a_3=a_((2)+1)=-5a_2-1=-5(-51)-1=254`

Finally, a₄ will be:

`a_4=a_((3)+1)=-5a_3-1=-5(254)-1=-1271`