This page focuses on the detailed Sequence and Series question answers for Class 11 Mathematics Sequence and Series, addressing the question: 'Find the sum of all numbers between 200 and 400 which are divisible by 7.'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.

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

Thus, the required sum is 8729.

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

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

- Q:-
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.
- Q:-
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.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - 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:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

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

- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.

- Q:-
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to

*n*terms of the G.P. - Q:-
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.

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

- Q:-
The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

- Q:-
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

- Q:-
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

- Q:-
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

- Q:-
Find the sum to

*n*terms of the sequence, 8, 88, 888, 8888… - Q:-
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)

- Q:-
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.

Harsh
2019-08-22 21:32:16

Good

saranya
2019-02-18 18:52:33

ummma thank you

Neelam
2019-01-07 13:03:24

But how I know that first no. Is 203

David N Maikundu
2018-11-09 16:44:45

thank you great elucidation

David N Maikundu
2018-11-09 16:32:27

wonderfull explanation

Shilpa
2018-09-20 12:53:07

Thank you for your help

DHARMAPADA KARUA
2018-06-03 11:06:42

Good solution.

Puru
2017-10-10 21:25:27

Thanks for the explanation

shethra krishna
2016-11-16 07:34:16

it was a wonderful explanation

karthik
2016-10-12 14:20:48

Good explanation

- NCERT Chapter