8. Sequences and Series
easy

एक अनंत गुणोत्तर श्रेणी, जिसका प्रथम पद $a$ तथा सार्वानुपात $r$ है, का योग $4$ तथा द्वितीय पद $3/4$ है, तब

A

$a = \frac{7}{4},\,r = \frac{3}{7}$

B

$a = \frac{3}{2},\,r = \frac{1}{2}$

C

$a = 2,\,r = \frac{3}{8}$

D

$a = 3,\,r = \frac{1}{4}$

(IIT-2000)

Solution

(d) यहाँ, $\frac{a}{{1 – r}} = 4$ एव $ar = \frac{3}{4}$

तब, $r(1 – r) = \frac{3}{{16}}$ या $16{r^2} – 16r + 3 = 0$

या $(4r – 3)(4r – 1) = 0$

$r = \frac{1}{4},\frac{3}{4}\,\,,{\rm{ }}$ एव  $a = 3,\,1$.

अत:, $(a,r) = \left( {3,\frac{1}{4}} \right)\,,\,\left( {1,\frac{3}{4}} \right)$.

Standard 11
Mathematics

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