8. Sequences and Series
easy

दिखाइए कि अनुक्रम $a, a r, a r^{2}, \ldots a r^{n-1}$ तथा $A , AR , AR ^{2}, \ldots AR ^{n-1}$ के संगत पदों के गुणनफल से बना अनुक्रम गुणोत्तर श्रेणी होती है तथा सार्व अनुपात ज्ञात कीजिए।

Option A
Option B
Option C
Option D

Solution

It has to be proved that the sequence: $a A, a r A R, a r^{2} A R^{2}, \ldots \ldots a r^{n-1} A R^{n-1},$ forms a $G.P.$

$\frac{{{\rm{ Second}}\,\,{\rm{term }}}}{{{\rm{ First }}\,\,{\rm{term }}}} = \frac{{ar\,AR}}{{a\,A}} = rR$

$\frac{{{\rm{ Third}}\,\,{\rm{ tem }}}}{{{\rm{ Second }}\,\,{\rm{term }}}} = \frac{{a{r^2}\,A{R^2}}}{{ar\,AR}} = rR$

Thus, the above sequence forms a $G.P.$ and the common ratio is $rR.$

Standard 11
Mathematics

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