Let the sum of n, 2n, 3n terms | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)

Answer:

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

Therefore,

S subscript 1 space equals space n over 2 open square brackets 2 a space plus space open parentheses n minus 1 close parentheses d close square brackets space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
S subscript 2 space equals space fraction numerator 2 n over denominator 2 end fraction open square brackets 2 a plus open parentheses 2 n minus 1 close parentheses d close square brackets space equals space n open square brackets 2 a space plus space open parentheses 2 n minus 1 close parentheses d close square brackets space space... left parenthesis 2 right parenthesis
S subscript 3 space equals space fraction numerator 3 n over denominator 2 end fraction open square brackets 2 a space plus space open parentheses 3 n minus 1 close parentheses d close square brackets space space space space space... left parenthesis 3 right parenthesis

From (1) and (2), we obtain

S subscript 2 space minus space S subscript 1 space equals n open square brackets 2 a space plus space open parentheses 2 n minus 1 close parentheses d close square brackets space minus n over 2 open square brackets 2 a space plus space open parentheses n minus 1 close parentheses d close square brackets
space space space space space space space space space space space space space space space space equals space n open curly brackets fraction numerator 4 a space plus space 4 n d space minus 2 d space minus 2 a space minus n d space plus d over denominator 2 end fraction close curly brackets
space space space space space space space space space space space space space space space space equals space n open square brackets fraction numerator 2 a space plus space 3 n d space minus d over denominator 2 end fraction close square brackets
space space space space space space space space space space space space space space space equals space n over 2 space open square brackets 2 a space plus space open parentheses 3 n minus 1 close parentheses d close square brackets
therefore space 3 open parentheses S subscript 2 space minus space S subscript 1 close parentheses space equals space fraction numerator 3 n over denominator 2 end fraction space open square brackets 2 a space plus space open parentheses 3 n minus 1 close parentheses d close square brackets equals S subscript 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets F r o m space left parenthesis 3 right parenthesis close square brackets

Hence, the given result is proved.


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

  • Rohit Raj
  • 2018-12-16 18:58:05

Awesome sir


  • Abhi
  • 2018-07-24 19:13:12

What a nice answer it is!


  • Neerav
  • 2016-10-23 17:28:18

how about if we solve this question like this... S1 = n S2 = n + 2n = 3n S3 = n + 2n + 3n = 6n according to question, S3 = 3(S2 -S1 ) by putting the value of S1, S2, S3 6n = 3(3n - n) 6n = 3(2n) 6n = 6n so, LHS = RHS Hence Proved


Comment(s) on this Question

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 3: Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show t....