Question

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

Please explain!

Answer 1

Answer:

$a_4=-1271$

Step-by-step 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:

$a_4=a_{(3)+1}=-5a_3-1=-5(254)-1=-1271$