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

Find the sum of all numbers between 200 | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Exercise 5, Question 4: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 4:

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

Answer:

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, … 399

∴First term, a = 203

Last term, l = 399

Common difference, d = 7

Let the number of terms of the A.P. be n.

∴ a_n = 399 = a + (n –1) d

⇒ 399 = 203 + (n –1) 7

⇒ 7 (n –1) = 196

⇒ n –1 = 28

⇒ n = 29

$therefore space S subscript 29 space equals space 29 over 2 space open parentheses 203 space plus space 399 close parentheses space space space space space space space space space space space space space equals space 29 over 2 space open parentheses 602 close parentheses space space space space space space space space space space space space space equals space open parentheses 29 close parentheses open parentheses 301 close parentheses space space space space space space space space space space space space space equals space 8729$

Thus, the required sum is 8729.

Other Questions of Chapter Sequence and Series

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

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

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.

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

Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.

Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

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

If the p^th, q^th and r^th terms of a G.P. are a, b and c, respectively. Prove that a^q-rb^r-pc^p-q=1

Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …

Q: Write the first five terms of the sequences whose nth term is a_n=n(n+2)

Popular questions of class 11 Mathematics

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

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.

Q: Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)
(ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6 upto infinity}
(v) {1, 4, 9, upto 100}

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

A point is in the XZ-plane. What can you say about its y-coordinate?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Recently Viewed Questions of Class 11 Mathematics

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

A point is in the XZ-plane. What can you say about its y-coordinate?

A point is on the x-axis. What are its y-coordinates and z-coordinates?

Find the equation of the circle with centre (0, 2) and radius 2

Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer.

Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Find the derivative of x² – 2 at x = 10.

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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Comments

Harsh
Aug 22, 2019

Good

saranya
Feb 18, 2019

ummma thank you

Neelam
Jan 07, 2019

But how I know that first no. Is 203

David N Maikundu
Nov 09, 2018

thank you great elucidation

David N Maikundu
Nov 09, 2018

wonderfull explanation

Shilpa
Sep 20, 2018

Thank you for your help

DHARMAPADA KARUA
Jun 03, 2018

Good solution.

Puru
Oct 10, 2017

Thanks for the explanation

shethra krishna
Nov 16, 2016

it was a wonderful explanation

karthik
Oct 12, 2016

Good explanation