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)

Show Answer

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),

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

पिछला

अगला

गोपनीयता नीति

द्वारा संचालित Prutor@IITK

sathee@iitk.ac.in

SATHEE का मीडिया कवरेज

खेल स्टोर

ऐप स्टोर

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

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.

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

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.