How do you find the sum of the infinite geometric series given #a_1=12#, r=-0.6?

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Answer 1 · 2017-10-13T17:51:32

The sum of the infinite geometric series is #7.50#.

Let us consider an infinite geometric series whose first term is #t_1# & common multiplier is #r#.

Then,

#t_1=a,t_2/t_1=r#.

#S_(oo)=a/(1-r)#..........(1).

Now given that,

#a=12# & #r=-0.6#

#:.r=-6/10#

#:.r=-3/5#

Now, applying formula (1) #rarr#

#S_(oo)=12/(1-(-3/5))#

#:.S_oo=12/(1+3/5)#

#:.S_oo=12/(8/5)#

#:.S_oo=(12xx5)/8#

#:.S_oo=15/2#

#:.S_oo=7(1/2)#

#:.S_oo=7.50#

Therefore, the sum of the infinite geometric series is #7.50#. (Answer).

Hope it Helps:)