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Calculate: $3+9+27+81+243+729+2187$.
Given: $3+9+27+81+243+729+2187$.
To do: To find the sum.
Solution:
As given, $3+9+27+81+243+729+2187$
It can be written as: $3^1+3^2+3^3+ .... + 3^7$
The given question is in G.P.
As known
$a_1=3$ [First term in the sequence]
$r=3$ [The common ratio]
$n=7$ [Number of terms]
On using these values in the Sum equation $S=a_1( \frac{( 1-r_n)}{( 1-r)}) =3( \frac{1-3^7}{1-3})$
$=3( \frac{1-2187}{1-3})$
$=3( \frac{-2186}{-2})$
$=3\times1093$
$=3279$
Thus, $3+9+27+81+243+729+2187=3279$.
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