Show that the sum of (m + n)th | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

Answer:

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

It is known that the kth term of an A. P. is given by

ak = a + (k –1) d

∴ am + n = a + (m + n –1) d

am – n = a + (m – n –1) d

am = a + (m –1) d

∴ am + n + am – n = a + (m + n –1) d + a + (m – n –1) d

= 2a + (m + n –1 + m – n –1) d

= 2a + (2m – 2) d

= 2a + 2 (m – 1) d

=2 [a + (m – 1) d]

= 2am

Thus, the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.

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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.

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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 1: Show that the sum of (m + n)th and (m – n)th terms of an A.P. is....

Show that the sum of (m + n)th | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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