geometric sequence

Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Answer 1

n^th term in geometric sequence is ar^n-1

a = first term, r = common ratio.

In the sequence 2^nd term is -21 and 5^th term is 567

2^nd term is ar^2-1 = -21

ar = -21 ---> (1)

And 5^th term is ar^5-1 = 567

ar⁴ = 567

(ar)r³ = 567

From (1) substitute the value of ar.

-21r³ = 567

r³  = 567/-21

r³  = -27

r³   = (-3)³

r = -3

Substitute the value of r in equation (1).

-3a = -21

a = 7

First term is 7.

n^th term is 7(-3)^n-1.