How do you find the explicit formula for the following sequence 0.2, -0.06, 0.018, -0.0054, 0.00162 ...?

1 Answer
Jun 28, 2016

Answer:

General Term #t_n=0.2(-0.3)^(n-1).#

Explanation:

Let us denote the #n^(th)# term of the given seq. by #t_n.#

Then, we find that, #t_2/t_1=-0.06/0.2=-0.3#
#t_3/t_2= -0.0.018/-0.06=-0.3#
# t_4/t_3-0.0054/0.018=-0.3,# & so on.

We conclude the it is a Geometric Seq. with first term #= t_1=a=0.2# and common ratio #=r=-0.3#

Its General Term is given by the formula #=t_n=a*r^(n-1),# i.e.,
#t_n=0.2(-0.3)^(n-1).#