Advertisements
Advertisements
प्रश्न
Divide 24 in three parts such that they are in AP and their product is 440.
Advertisements
उत्तर
Let the required parts of 24 be (a- d) , a and (a +d) such that they are in AP.
Then (a-d) + a+ (a +d) = 24
⇒ 3a = 24
⇒ a=8
Also , (a-d) .a. (a+d) = 440
⇒ `a(a^2 - d^2 )= 440`
⇒` 8(64 - d^2 ) = 440`
⇒`d^2 = 64 - 55 = 9`
⇒ `d= +-3`
Thus , a = 8 and d = `+-3`
Hence, the required parts of 24 are (5,8,11) or (11,8,5).
APPEARS IN
संबंधित प्रश्न
In an AP given l = 28, S = 144, and there are total 9 terms. Find a.
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.
Which term of the AP 21, 18, 15, …… is -81?
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
Write an A.P. whose first term is a and common difference is d in the following.
a = –19, d = –4
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
Write the sum of first n odd natural numbers.
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
Find the sum of all members from 50 to 250 which divisible by 6 and find t13.
What is the sum of an odd numbers between 1 to 50?
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
