Advertisements
Advertisements
Question
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Advertisements
Solution
In the given problem, the sum of three terms of an A.P is 27 and the product of the three terms is 648. We need to find the three terms.
Here,
Let the three terms be (a - d), a, (a + d) where a is the first term and d is the common difference of the A.P
So,
(a - d) + a(a + d) = 27
3a = 27
a = 9 ......(1)
Also
(a - d)a(a + d) = a + 6
`a(a^2 - d^2) = 648` [Using `a^2 - b^2 = (a + b)(a - b)`]
`9(9^2 - d^2) = 648`
`81 - d^2 = 72`
Further solving for d
`81 - d^2 =72`
`81 - 72 = d62`
`81 - d^2 = 72`
Further solving for d
`81 - d^2 = 72`
`81 - 72 = d^2`
`d = sqrt9`
d = 3....(2)
Now, substituting (1) and (2) in three terms
First term = a - d
So, a - d = 9 - 3
= 6
Also
Second term = a
So,
a= 9
Also
Third term = a + d
So
a + d = 9 + 3
= 12
Therefore the three term are 6, 9 and 12
RELATED QUESTIONS
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
The first term of an AP is p and its common difference is q. Find its 10th term.
If (2p +1), 13, (5p -3) are in AP, find the value of p.
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 an given A.P., t7 = 4, d = −4, then a = ______.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
Simplify `sqrt(50)`
Write the sum of first n odd natural numbers.
If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a.
If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
Q.6
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
