Advertisements
Advertisements
Question
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
Advertisements
Solution
Let the three numbers be a – d, a and a + d.
According to the question,
\[\left( a - d \right) + a + \left( a + d \right) = 207\]
\[ \Rightarrow 3a = 207\]
\[ \Rightarrow a = 69\]
Also,
\[\left( a - d \right)a = 4623\]
\[ \Rightarrow \left( 69 - d \right)\left( 69 \right) = 4623\]
\[ \Rightarrow 69 - d = \frac{4623}{69}\]
\[ \Rightarrow 69 - d = 67\]
\[ \Rightarrow 69 - 67 = d\]
\[ \Rightarrow d = 2\]
Hence, the three numbers are 67, 69 and 71.
APPEARS IN
RELATED QUESTIONS
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
Find how many integers between 200 and 500 are divisible by 8.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
How many two-digit number are divisible by 6?
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Write the value of x for which 2x, x + 10 and 3x + 2 are in 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 sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
The sum of first five multiples of 3 is ______.
In an AP, if Sn = n(4n + 1), find the AP.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
