What is the 6th term of this geometric sequence 3, –9, 27, –81, …?

1 Answer
Jun 29, 2015

color(blue)(-729

Explanation:

the geometric sequence given is:
3 , -9 , 27 , -81 ...

When provided with a geometric sequence we must first calculate the common ratio r
r is obtained by dividing a term by its preceding term
1) -9/3 =-3
2) 27/-9 = -3

for this sequence the common ratio r = -3 the first term a = 3
and n = 6

The 6th term can be obtained through formula
T_n = ar^(n-1) = 3 xx -3^((6-1))
= 3xx -3^5
= 3 xx -243= color(blue)(-729