Advertisements
Advertisements
Question
Divide 24 in three parts such that they are in AP and their product is 440.
Advertisements
Solution
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
RELATED QUESTIONS
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
Find the middle term of the AP 6, 13, 20, …., 216.
Find the middle term of the AP 10, 7, 4, ……., (-62).
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
If the first term of an A.P. is a and nth term is b, then its common difference is
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
Find S10 if a = 6 and d = 3
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
