Sum of first 'n' terms of a G.P.
Category : JEE Main & Advanced
If \[a\] be the first term, \[r\] the common ratio, then sum \[{{S}_{n}}\] of first \[n\] terms of a G.P. is given by
\[{{S}_{n}}=\frac{a(1-{{r}^{n}})}{1-r}\] and \[{{S}_{n}}=\frac{a-lr}{1-r}\], (when \[|r|\,<1\])
\[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}\] and \[{{S}_{n}}=\frac{lr-a}{r-1}\], (when \[|r|\,>1\])
\[{{S}_{n}}=na\], (when \[r=1\])
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