SATHEE: Sequences and Series 4 Question 8

Sequences and Series 4 Question 8

8.

Consider an infinite geometric series with first term $a$ and common ratio $r$ . If its sum is 4 and the second term is $3 / 4$ , then

(2000, 2M)

(a) $a = 4 / 7, r = 3 / 7$

(b) $a = 2, r = 3 / 8$

(d) $a = 3, r = 1 / 4$

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Answer:

Correct Answer: 8. (d)

Solution:

Since, sum $= 4$ and second term $= \frac{3}{4}$ .

It is given first term $a$ and common ratio $r$ .

$\begin{aligned} \Rightarrow \frac{a}{1 - r} = 4, ar = \frac{3}{4} \\ \Rightarrow r = \frac{3}{4 a} \\ \Rightarrow \frac{a}{1 - \frac{3}{4 a}} = 4 \\ \Rightarrow \frac{4 a^{2}}{4 a - 3} = 4 \\ \Rightarrow (a - 1) (a - 3) = 0 \\ \Rightarrow a = 1 or 3 \end{aligned}$

When $a = 1, r = 3 / 4$

and when $a = 3, r = 1 / 4$

Sequences and Series 4 Question 8

8.

Answer:

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Sequences and Series 4 Question 8

8.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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