How do you find the sum of the finite geometric sequence of #Sigma 10(1/5)^n# from n=0 to 20?

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Answer 1 · 2017-10-13T21:22:11

#12.45# (2 .d.p)

First calculate the first three terms:

#10(1/5)^0=color(blue)(10) , 10(1/5)^1= color(blue)(2) , 10(1/5)^2= color(blue)(2/5)#

Find the common ratio:

#2/10 = (2/5)/2=1/5#

The sum of a geometric sequence is:

#a((1-r^n)/(1-r))#

Where a is the first term, n is the nth term and r is the common ratio.

So:

#10((1-(1/5)^20)/(1-(1/5)))=12.4999999999999737856#