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8. Sequences and Series
easy
यदि गुणोत्तर श्रेणी $\left\{ {{a_n}} \right\}$ में,$\;{a_1} = 3,\;{a_n} = 96$ व ${S_n} = 189$, तब $n$ का मान है
A
$5$
B
$6$
C
$7$
D
$8$
Solution
(b) ${a_1} = 3,\;{a_n} = 96$
$ \Rightarrow $${a_1}{r^{n – 1}} = 96$
$ \Rightarrow $${r^{n – 1}} = 32$ ……(i)
अब, ${S_n} = \frac{{{a_1}({r^n} – 1)}}{{r – 1}} = 189$
$ \Rightarrow $$\frac{{3(32r – 1)}}{{r – 1}} = 189$ ,
(समीकरण (i) से)
अत: $r = 2$ एवं $n = 6$.
Standard 11
Mathematics