Gujarati
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

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