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

1 Answer
Jun 29, 2015

Answer:

# 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#