How do you find $a_3$ for the geometric series given $S_n=249.92$ , r=0.2, n=5?

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Answer 1 · 2017-11-21T12:23:18

$a_3=8$

$S_n=249.92 , r =0.2 , n=5$

$S_n= a_1 *(1-r^n)/(1-r)$

$:. 249.92= a_1 *(1-0.2^5)/(1-0.2)$

$:. a_1 = {249.92*(1-0.2)}/ (1-0.2^5)=200$

First term is $a_1=200$

Third term is $a_3=a_1 * r ^(n-1)= 200 * (0.2)^(3-1)$ or

$a_3== 200 * (0.2)^2=200* 0.04=8$

$:. a_3=8$ [Ans]

How do you find a_3a_3 for the geometric series given S_n=249.92S_n=249.92, r=0.2, n=5?