Question 1161642


In General we write a Geometric Sequence like this:

{ {{{a}}}, {{{ar}}},{{{ ar^2}}}, {{{ar^3}}}, ... }

where:

{{{a}}} is the first term, and
{{{r}}} is the factor between the terms (called the "common ratio")

If the first term of a geometric sequence is {{{0.9}}} and it's ratio is{{{ 0.8}}}, we have

{{{a=0.9}}}
{{{r=0.8}}}

and first five terms are:

{{{a=0.9}}}
{{{ar=0.9*0.8=0.72}}}
{{{ar^2=0.9*0.8^2=0.576}}}
{{{ar^3=0.9*0.8^3=0.4608}}}
{{{ar^4=0.9*0.8^4=0.36864}}}

their sum is:
{{{sum=0.9+0.72+0.576+0.4608+0.36864=3.02544}}}

or, use sum formula

{{{sum=a((1-r^n)/(1-r))}}}......substitute given

{{{sum=0.9((1-0.8^n)/(1-0.8))}}}

fifth term->{{{n=5}}}

 the sum of the first five terms, will be

{{{sum=0.9((1-0.8^5)/(1-0.8))}}}

{{{sum=0.9((1-0.32768)/0.2)}}}

{{{sum=0.9(0.67232/0.2)}}}

{{{sum=0.9(3.3616)}}}

{{{sum=3.02544}}}