If the first and the nth term | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.

Answer:

The first term of the G.P is a and the last term is b.

Therefore, the G.P. is a, ar, ar2, ar3, … arn–1, where r is the common ratio.

b = arn–1 … (1)

P = Product of n terms

= (a) (ar) (ar2) … (arn–1)

= (a × a ×…a) (r × r2 × …rn–1)

= an r 1 + 2 +…(n–1) … (2)

Here, 1, 2, …(n – 1) is an A.P.

∴1 + 2 + ……….+ (n – 1)

equals fraction numerator n minus 1 over denominator 2 end fraction open square brackets 2 plus left parenthesis n minus 1 minus 1 right parenthesis cross times 1 close square brackets equals fraction numerator n minus 1 over denominator 2 end fraction open square brackets 2 plus n minus 2 close square brackets equals fraction numerator n open parentheses n minus 1 close parentheses over denominator 2 end fraction P space equals space a to the power of n r to the power of fraction numerator n open parentheses n minus 1 close parentheses over denominator 2 end fraction end exponent therefore space P squared space equals space a to the power of 2 n end exponent space r to the power of n open parentheses n minus 1 close parentheses end exponent space space space space space space space space space space space space equals space open square brackets a squared space r to the power of left parenthesis n minus 1 right parenthesis end exponent close square brackets to the power of n space space space space space space space space space space space space equals open square brackets a cross times a r to the power of n minus 1 end exponent close square brackets to the power of n space space space space space space space space space space space space equals open parentheses a b close parentheses to the power of n 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 space space space space space space open square brackets U sin g space left parenthesis 1 right parenthesis close square brackets

Thus, the given result is proved.


< 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

  • Nafeesa
  • 2019-10-30 19:06:29

Thank you

  • Aniska Chatterjee
  • 2019-07-28 08:25:27

Very good.. thanks for the easiest way.

  • Hitesh Kumar
  • 2019-05-04 15:52:24

Very good

  • Yash
  • 2019-02-09 12:56:13

Please change the colour of this page And nice explanation

  • Pranav
  • 2019-02-06 23:30:16

Why n-1/2 is taken instead of n/2

  • Ravi Ranjan
  • 2018-09-02 00:54:54

Change the colour of the page

  • Param
  • 2018-06-27 23:56:10

Good

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 23: If the first and the nth term of a G.P. are a ad b, respectively, and if&nb....

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