Find the value of n so that&nb | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Find the value of n so that fraction numerator a to the power of n plus 1 end exponent space plus space b to the power of n plus 1 end exponent over denominator a to the power of n space plus space b to the power of n end fraction may be the geometric mean between a and b.

Answer:

G. M. of a and b is square root of a b end root.

By the given condition, fraction numerator a to the power of n plus 1 end exponent space plus space b to the power of n plus 1 end exponent over denominator a to the power of n space plus space b to the power of n end fraction equals square root of a b end root

Squaring both sides, we obtain

open parentheses a to the power of n plus 1 end exponent space plus space b to the power of n plus 1 end exponent close parentheses squared over open parentheses a to the power of n space plus space b to the power of n close parentheses squared equals a b rightwards double arrow a to the power of 2 n plus 2 end exponent space plus space 2 a to the power of n plus 1 end exponent b to the power of n plus 1 end exponent space plus space b to the power of 2 n plus 2 end exponent space equals space open parentheses a b close parentheses open parentheses a to the power of 2 n end exponent space plus space 2 a to the power of n b to the power of n space plus space b to the power of 2 n end exponent close parentheses rightwards double arrow a to the power of 2 n plus 2 end exponent space plus space 2 a to the power of n plus 1 end exponent b to the power of n plus 1 end exponent space plus space b to the power of 2 n plus 2 end exponent space equals space a to the power of 2 n plus 1 end exponent b space plus space 2 a to the power of n plus 1 end exponent b to the power of n plus 1 end exponent space plus space a b to the power of 2 n plus 1 end exponent rightwards double arrow a to the power of 2 n plus 2 end exponent space plus space b to the power of 2 n plus 2 end exponent space equals space a to the power of 2 n plus 1 end exponent b space plus space a b to the power of 2 n plus 1 end exponent rightwards double arrow a to the power of 2 n plus 2 end exponent space minus a to the power of 2 n plus 1 end exponent b space equals space a b to the power of 2 n plus 1 end exponent space minus space b to the power of 2 n plus 2 end exponent rightwards double arrow space a to the power of 2 n plus 1 end exponent open parentheses a minus b close parentheses equals b to the power of 2 n plus 1 end exponent open parentheses a minus b close parentheses rightwards double arrow open parentheses a over b close parentheses to the power of 2 n plus 1 end exponent space equals space 1 space equals space open parentheses a over b close parentheses to the power of 0 rightwards double arrow 2 n space plus 1 space equals space 0 rightwards double arrow n space equals space fraction numerator minus 1 over denominator 2 end fraction

 


< Previous Question

Next Question >

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

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 3 , Question 27: Find the value of n so that  may be the geometric mean between a and&n....

Chapters for Class 11 Mathematics

Subjects for Class 11


Notice: Undefined index: pageType in /var/www/html/ss_beta/saralstudy/ss_new/web/template/common/class_sidebar.php on line 45

Students Also Read

Important links

Quick Links

Resources

Support