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The ratio of the sums of m and n terms of an A.P. ...

The ratio of the sums of m and | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nth term is (2m – 1): (2n – 1).

Answer:

Let a and b be the first term and the common difference of the A.P. respectively.

According to the given condition,

$fraction numerator S u m space o f space m space t e r m s over denominator s u m space o f space n space t e r m s end fraction equals m squared over n squared rightwards double arrow fraction numerator begin display style m over 2 end style open square brackets 2 a plus open parentheses m minus 1 close parentheses d close square brackets over denominator begin display style n over 2 end style open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets end fraction equals m squared over n squared rightwards double arrow space space space fraction numerator 2 a plus left parenthesis m minus 1 right parenthesis d over denominator 2 a plus left parenthesis n minus 1 right parenthesis d end fraction equals m over n space space space space space.... left parenthesis 1 right parenthesis P u t t i n g space m space equals space 2 m space � space 1 space a n d space n space equals space 2 n space � space 1 space i n space left parenthesis 1 right parenthesis comma space w e space o b t a i n fraction numerator 2 a plus left parenthesis 2 m minus 2 right parenthesis d over denominator 2 a plus left parenthesis 2 n minus 2 right parenthesis d end fraction equals fraction numerator 2 m minus 1 over denominator 2 n minus 1 end fraction rightwards double arrow fraction numerator a plus left parenthesis m minus 1 right parenthesis d over denominator a plus left parenthesis n minus 1 right parenthesis d end fraction equals fraction numerator 2 m minus 1 over denominator 2 n minus 1 end fraction space space space space.... left parenthesis 2 right parenthesis fraction numerator m to the power of t h end exponent t e r m space o f space A. P. over denominator n to the power of t h space end exponent t e r m space o f space A. P. end fraction equals fraction numerator a plus left parenthesis m minus 1 right parenthesis d over denominator a plus left parenthesis n minus 1 right parenthesis d end fraction space space space space... left parenthesis 3 right parenthesis F r o m space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space o b t a i n fraction numerator m to the power of t h end exponent t e r m space o f space A. P. over denominator n to the power of t h space end exponent t e r m space o f space A. P. end fraction equals fraction numerator 2 m minus 1 over denominator 2 n minus 1 end fraction T h u s comma space t h e space g i v e n space r e s u l t space i s space p r o v e d.$

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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Ajsgs
2019-07-20 19:18:02

It is a concept of gp

Subham Kumar
2019-02-24 10:51:05

Why we put m=2m-1 and n=2n-1 in (1)

Rehina
2018-11-28 19:40:02

Thanks for your tip thnq soooo much

Lucky
2017-01-12 05:54:55

Good question

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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 2 , Question 12: The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that....

The ratio of the sums of m and | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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