Class 11 Mathematics - Chapter Sequence and Series NCERT Solutions | Find the sum of integers from 1 to 100 t
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
The integers from 1 to 100, which are divisible by 2, are 2, 4, 6… 100.
This forms an A.P. with both the first term and common difference equal to 2.
⇒100 = 2 + (n –1) 2
⇒ n = 50
The integers from 1 to 100, which are divisible by 5, are 5, 10… 100.
This forms an A.P. with both the first term and common difference equal to 5.
∴100 = 5 + (n –1) 5
⇒ 5n = 100
⇒ n = 20
The integers, which are divisible by both 2 and 5, are 10, 20, … 100.
This also forms an A.P. with both the first term and common difference equal to 10.
∴100 = 10 + (n –1) (10)
⇒ 100 = 10n
⇒ n = 10
∴Required sum = 2550 + 1050 – 550 = 3050
Thus, the sum of the integers from 1 to 100, which are divisible by 2 or 5, is 3050.
More Questions From Class 11 Mathematics - Chapter Sequence and Series
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
- 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, 32, 33, … are needed to give the sum 120?
- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.
- 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 difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
- Q:-
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.
Popular Questions of Class 11 Mathematics
- Q:-
Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer. - Q:-
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
- Q:-
A point is on the x-axis. What are its y-coordinates and z-coordinates?
- Q:-
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?
- Q:-
Find the equation of the circle with centre (0, 2) and radius 2
- Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.
- 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:-
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
- Q:-
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.
- Q:-
A point is in the XZ-plane. What can you say about its y-coordinate?
Recently Viewed Questions of Class 11 Mathematics
- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
- Q:-
A point is in the XZ-plane. What can you say about its y-coordinate?
- 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:- 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:-
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
- Q:-
A point is on the x-axis. What are its y-coordinates and z-coordinates?
- 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} - Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.
- Q:-
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
- Q:- Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:
(i) 5__A
(ii) 8__A
(iii) 0__A
(iv) 4__A
(v) 2__A
(vi) 10__A
10 Comment(s) on this Question
The answer was helpful but can we write directly the integers divisible by both 2 or 5??
The answer was helpful but can we write directly the integers divisible by both 2 or 5??
Thanks for the solution.
That is correct but I have asked other answer
Great..
Thanks sir it helped me
thanks sir.. ... wonderful answer.....
Thanks a lot
Thanks sir
Can it be solved by n(n+2)/2
- All Chapters Of Class 11 Mathematics
- All Subjects Of Class 11