Welcome to the NCERT Solutions for Class 11th Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Exercise 5, Question 2: **if the sum of three numbers in a p is 24 and the...**.

Question 2

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

Answer

Let the three numbers in A.P. be *a* – *d*, *a*, and *a* + *d*.

According to the given information,

(*a* – *d*) + (*a*) + (*a* + *d*) = 24 … (1)

⇒ 3*a* = 24

∴ *a* = 8

(*a* – *d*) *a* (*a* + *d*) = 440 … (2)

⇒ (8 – *d*) (8) (8 + *d*) = 440

⇒ (8 – *d*) (8 + *d*) = 55

⇒ 64 – *d*2 = 55

⇒ *d*2 = 64 – 55 = 9

⇒ *d *= ± 3

Therefore, when *d* = 3, the numbers are 5, 8, and 11 and when *d* = –3, the numbers are 11, 8, and 5.

Thus, the three numbers are 5, 8, and 11.

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

- 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:-
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

*n*th term of a G.P. are*a*ad*b*, respectively, and if*P*is the product of*n*terms, prove that*P*^{2}= (*ab*)^{n}.

- 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?

- Q:-
Describe the sample space for the indicated experiment: A die is thrown two times.

- Q:-
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

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

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

- 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:-
A point is in the XZ-plane. What can you say about its

*y*-coordinate? - Q:-
How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

- 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:-
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 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.

Asif
2019-12-15 20:19:13

Thnx

Asif
2019-12-15 20:18:38

Thnx

Deekshitha
2019-09-04 18:24:24

Thank you it for solving the problem and helped me

Deekshitha
2019-09-04 18:24:01

Thank you it for solving the problem and helped me

KICCHA balaji
2019-03-12 23:10:08

Tq bro Usefullll

Nikhil
2019-03-04 14:58:14

Thanx

QAMAR
2016-11-17 12:23:41

HOW CAN WE TAKE NUMBER I MEAN ON WHICH BASES

Mabel
2016-01-17 00:57:58

I luv dis.. Its easier and explanatory. Thanks!

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