JEE Main & Advanced Mathematics Geometric Progression Sum of first 'n' terms of a G.P.

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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