Question

What is the sum of the geometric series in which a1 = 7 , r = 3 and an = 1701?
Sn = 2,548
Sn = 851
Sn = 58,824
Sn = −851

Answer 1

find n by the formula
\[a _{n}=a _{1}r ^{n-1}\]
find n
then
\[S _{n}=a _{1}\frac{ r^n-1 }{ r-1 }\]

Answer 2

\[1701=7*3^{n-1}\]
\[3^{n-1}=\frac{ 1701 }{ 7 }=243=3^5,n-1=5,n=5+1=6\]
\[S _{n}=7\frac{ 3^n-1 }{ 3-1 }=7\frac{ 3^6-1 }{ 3-1 }=7\frac{ 729-1 }{ 2 }=?\]