How do you find $S_n$ for the geometric series $a_1=2$ , $a_6=486$ , r=3?

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Answer 1 · 2017-05-10T10:40:48

Sum of the series for $6$ terms is $728$

Number of term of geometric series is $n=6$

Common ratio of geometric series is $r=3$

1st term of geometric series is $a_1=2$

6th term of geometric series is $a_6= a_1* r^(n-1) =2*3^(6-1)=2*3^5= 486$

Sum of the series formula : $S_n = a_1* ((1-r^n)/(1-r))$

Sum of the series for $6$ terms : $S_6 = 2* ((1-3^6)/(1-3)) =$

$cancel2* ((1-3^6)/ cancel(-2)) = - (1-3^6) = -(1-729) =728$ [Ans]

How do you find S_nS_n for the geometric series a_1=2a_1=2, a_6=486a_6=486, r=3?