Question

If a₁ = 5 and an+1 = -3an -3 then find a4

Answer 1

Using the recursive formula an+1 = -3an - 3 and starting with a1 = 5, the subsequent terms are calculated until the fourth term (a4) is found to be -156.

Step-by-step explanation:

To find the fourth term (a4) of the given sequence, we need to use the recursive formula provided: a1 = 5 and an+1 = -3an - 3. We will calculate the terms one by one until we reach a4.

First, we find a2:

a2 = -3a1 - 3

= -3(5) - 3

= -15 - 3

= -18

Next, we calculate a3:

a3 = -3a2 - 3

= -3(-18) - 3

= 54 - 3

= 51

Finally, we calculate a4:

a4 = -3a3 - 3

= -3(51) - 3

= -153 - 3

= -156

Therefore, the fourth term of the sequence, a4, is -156.