Home
NCERT Soltions
Class 11
Mathematics
Sequence and Series
Between 1 and 31, m numbers have been inserted in such a way...

Between 1 and 31, m numbers ha | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)thnumbers is 5:9. Find the value of m.

Answer:

Let A1, A2, … Am be m numbers such that 1, A1, A2, … Am, 31 is an A.P.

Here, a = 1, b = 31, n = m + 2

∴ 31 = 1 + (m + 2 – 1) (d)

⇒ 30 = (m + 1) d

$rightwards double arrow d equals fraction numerator 30 over denominator m plus 1 end fraction space space space space space space space space... left parenthesis 1 right parenthesis$

A1 = a + d

A2 = a + 2d

A3 = a + 3d …

∴ A7 = a + 7d

Am–1 = a + (m – 1) d

According to the given condition,

$fraction numerator a plus 7 d over denominator a plus open parentheses m minus 1 close parentheses d end fraction equals 5 over 9 rightwards double arrow fraction numerator 1 plus 7 open parentheses begin display style fraction numerator 30 over denominator open parentheses m plus 1 close parentheses end fraction end style close parentheses over denominator 1 plus open parentheses m minus 1 close parentheses open parentheses begin display style fraction numerator 30 over denominator m plus 1 end fraction end style close parentheses end fraction equals 5 over 9 space space space space space space space space space space space space space space space space open square brackets F r o m space left parenthesis 1 right parenthesis close square brackets rightwards double arrow fraction numerator m plus 1 plus 7 open parentheses 30 close parentheses over denominator m plus 1 plus 30 open parentheses m minus 1 close parentheses end fraction equals 5 over 9 rightwards double arrow fraction numerator m plus 1 plus 210 over denominator m plus 1 plus 30 m minus 30 end fraction equals 5 over 9 rightwards double arrow fraction numerator m plus 211 over denominator 31 m space minus 29 end fraction equals 5 over 9 rightwards double arrow 9 m space plus space 1899 space equals space 155 m space minus 145 rightwards double arrow 155 m space minus 9 m space equals space 1899 space plus 145 rightwards double arrow 146 m equals 2044 rightwards double arrow m equals 14$

Thus, the value of m is 14.

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

Popular questions of class 11 Mathematics

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Q: Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Recently Viewed Questions of Class 11 Mathematics

Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Q: In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55
Number 5 6 12 14 26 12 16 9

Give three examples of sentences which are not statements. Give reasons for the answers.

Q: If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term

Solve each of the following equations:

x² + 3 = 0

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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

Find the sum to n terms of the series whose nth terms is given by (2n – 1)²

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 2 , Question 16: Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence i....

Between 1 and 31, m numbers ha | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

< Previous Question

Next Question >

Popular questions of class 11 Mathematics

Recently Viewed Questions of Class 11 Mathematics

Study Tips for Answering NCERT Questions:

Comments

Comment(s) on this Question

Chapters for Class 11 Mathematics

Subjects for Class 11

Students Also Read

Important links

Quick Links

Resources

Support