The sum of the series 2+6+18+54+...+39366 is 59048
The given series is:
2+6+18+54+...+39366
This is a geometric series with the common ratio:
r = 6/2
r = 2
The nth term of a geometric series is given as:
[tex]T_n = ar^{n-1}\\\\T_n = 2(3)^{n-1}\\\\3^{n-1} = \frac{39366}{2} \\\\3^{n-1} = 19684\\\\3^{n-1} = 3^9\\\\n-1 = 9\\\\n = 9+1\\\\n = 10[/tex]
There are 10 terms in the series
The sum of the series will be given as:
[tex]S_n = \frac{a(r^{n}-1)}{r-1} \\\\S_{10} = \frac{2(3^{10}-1)}{3-1}\\\\S_{10} = \frac{2(3^{10}-1)}{2}\\\\S_{10} = 3^{10}-1\\\\S_{10} = 59049-1\\\\S_{10} = 59048[/tex]
The sum of the series 2+6+18+54+...+39366 is 59048
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