How do you find the first term of a geometric sequence whose fourth term is -6 and whose common ratio is 1/3?

1 Answer
Nov 20, 2015

Answer:

The first term is #(-162)#

Explanation:

Suppose the first term is #a_1#
then (since the common ratio is #1/3#)

#color(white)("XXX")a_2= (1/3)xxa_1#

#color(white)("XXX")a_3= (1/3)xxa_2 = (1/3)^2xxa_1#

#color(white)("XXX")a_4= (1/3)xxa_3 = (1/3)^3xxa_1#

We are told
#color(white)("XXX")a_4 = -6#

So
#color(white)("XXX")(1/3)^3xxa_1=-6#

#color(white)("XXX")1/27xxa_1 =-6#

#color(white)("XXX")a_1=(-6)xx27 = -162#