SATHEE: Sequences and Series 3 Question 14

Sequences and Series 3 Question 14

14.

Find three numbers $a, b, c$ between 2 and 18 such that (i) their sum is 25 . (ii) the numbers $2, a, b$ are consecutive terms of an AP. (iii) the numbers $b, c, 18$ are consecutive terms of a GP.

(1983, 2M)

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Answer:

Correct Answer: 14. $(a = 5) (b = 8) (c = 12)$

Solution:

If $a, b, c \in (2, 18)$ , then

$a + b + c = 25$

Since, $2, a, b$ are in AP.

$\Rightarrow 2 a = b + 2$

and $b, c, 18$ are in GP.

$\Rightarrow c^{2} = 18 b$

From Eqs. (i), (ii) and (iii),

$\begin{aligned} \frac{b + 2}{2} + b + \sqrt{18 b} = 25 \\ \Rightarrow 3 b + 2 + 6 \sqrt{2} \sqrt{b} = 50 \\ \Rightarrow 3 b + 6 \sqrt{2} \sqrt{b} - 48 = 0 \\ \Rightarrow b + 2 \sqrt{2} \sqrt{b} - 16 = 0 \\ \Rightarrow b + 4 \sqrt{2} \sqrt{b} - 2 \sqrt{2} \sqrt{b} - 16 = 0 \\ \Rightarrow \sqrt{b} (\sqrt{b} + 4 \sqrt{2}) - 2 \sqrt{2} (\sqrt{b} + 4 \sqrt{2}) = 0 \\ \Rightarrow (\sqrt{b} - 2 \sqrt{2}) (\sqrt{b} + 4 \sqrt{2}) = 0 \\ \Rightarrow b = 8, a = 5 \\ and c = 12 \end{aligned}$

Sequences and Series 3 Question 14

14.

Answer:

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Sequences and Series 3 Question 14

14.

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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