A G.P. consists of an even number of ter | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Answer:

Let the G.P. be T₁, T₂, T₃, T₄, … T_2n.

Number of terms = 2n

According to the given condition,

T₁ + T₂ + T₃ + …+ T_2n = 5 [T₁ + T₃ + … +T_2n–1]

⇒ T₁ + T₂ + T₃ + … + T_{2n – 5} [T₁ + T₃ + … + T_2n–1] = 0

⇒ T₂ + T₄ + … + T_2n = 4 [T₁ + T₃ + … + T_2n–1]

Let the G.P. be a, ar, ar², ar³, …

$therefore space fraction numerator a r space open parentheses r to the power of n space minus 1 close parentheses over denominator r minus 1 end fraction space equals space fraction numerator 4 space cross times space a open parentheses r to the power of n space minus 1 close parentheses over denominator r space minus 1 end fraction rightwards double arrow a r space equals space 4 a rightwards double arrow r space equals space 4$

Thus, the common ratio of the G.P. is 4.

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Comments

Segalla
2017-06-30 22:58:20

Thank u it was very helpfull

Hacker
2017-06-27 21:06:11

Its Helpful

Aditya Kumar
2017-06-20 13:52:43

Yes the process is correct and the answer as well,but there is a mistake.If it is taken that the original g.p is a,ar^2,a^3... the common ratio between the odd terms and even terms should be r^2.

Bikash
2016-09-20 13:37:27

Thank u

ami
2016-04-18 10:17:04

Thank you

satarupa
2015-03-12 11:42:51

it was very helpful!!!!

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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 5 , Question 11: A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms ....

A G.P. consists of an even number of ter | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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