Recursive Sequences

Question

If a_1=4a1​=4 and a_n=-3a_{n-1}an​=−3an−1​ then find the value of a_4a4​.

Answer 1

a₄ = a₁(r)^n-1

a₄ = 4(-3)³

Can you compute and answer>

Answer 2

an= -3an-1

a1 = 4

a2 = -3a1= -3(4)=-12

a3 =-3a2 =-3(-12) =36

a4 = -3a3 =-3(36) = -108

4,-12,36,-108, ...

It's a geometric sequence with common ratio = r = -3

an= a1(r^(n-1))

an = 4(-3^(n-1))

a4 = 4(-3^(4-1))

a4 = 4(-3^(3)) = 4(-27) = =108

a4 = -108

4th term of the sequence = -108