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If the 4th, 10th and 16th terms of a G.P. are x, y ...

If the 4th, 10th and 16th term | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Answer:

Let a be the first term and r be the common ratio of the G.P.

According to the given condition,

a₄ = a r³ = x … (1)

a₁₀ = a r⁹ = y … (2)

a₁₆ = a r¹⁵ = z … (3)

Dividing (2) by (1), we obtain

$y over x space equals space fraction numerator a r to the power of 9 over denominator a r cubed end fraction space rightwards double arrow y over x space equals space r to the power of 6$

Dividing (3) by (2), we obtain

$z over y space equals space fraction numerator a r to the power of 15 over denominator a r to the power of 9 end fraction rightwards double arrow z over y equals r to the power of 6$

∴ $y over x space equals space z over y$

Thus, x, y, z are in G. P.

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Comments

Pranshu krishan
2017-10-02 19:09:43

Thanks easy to learn!!!!!

sarthak tripathi
2017-08-13 19:46:05

nice solution ticki

bandhana
2017-02-24 17:07:23

Thanks , really its very helpful for me

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 17: If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Pro....

If the 4th, 10th and 16th term | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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