If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
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)
⇒ 3a = 24
∴ a = 8
(a – d) a (a + d) = 440 … (2)
⇒ (8 – d) (8) (8 + d) = 440
⇒ (8 – d) (8 + d) = 55
⇒ 64 – d2 = 55
⇒ d2 = 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.
Popular Questions of Class 11 Mathematics
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- 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, 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:- 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.
Recently Viewed Questions of Class 11 Mathematics
- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
- 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:-
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
- Q:-
Find the derivative of x2 – 2 at x = 10.
- Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
- 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:-
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.
- 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.
- Q:-
Evaluate
8 Comment(s) on this Question
Thnx
Thnx
Thank you it for solving the problem and helped me
Thank you it for solving the problem and helped me
Tq bro Usefullll
Thanx
HOW CAN WE TAKE NUMBER I MEAN ON WHICH BASES
I luv dis.. Its easier and explanatory. Thanks!
- NCERT Chapter