If the sum of 3 positive integers of an AP is 24 then the first term is
Answers
COMPLETE QUESTION WILL BE
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
SOL:-
Let the three numbers in A.P. be a−d,a, and a+d
According to given information
Sum=(a−d)+(a)+(a+d)=24...(1)
⇒3a=24∴a=8
& Product=(a−d)a(a+d)=440...(2)
⇒(8−d)(8)(8+d)=440
⇒(8−d)(8+d)=55
⇒64−d
2
=55
⇒d
2
=64−55=9
⇒d=±3
Therefore when d=3, the numbers are 5,8,11 and
when d=−3, the numbers are 11,8 and 5.
Thus the three numbers are 5,8 and 11.
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Given : sum of 3 positive integers of an AP is 24
To find : first term
Solution:
sum of 3 positive integers of an AP is 24
Let say
3 positive integers in AP are
a - d , a , a + d
Sum = 24
=> (a - d) + a + (a + d) = 24
=>3a = 24
=> a = 8
Looks like some data is missing
As we do not have any information other than all term being positive integer
So many Solution possible
Hence d can have values from 1 to 7 & -1 to - 7
Hence
First term can be from
8 - 1 to 8 - 7 & 8 -(-1) to 8-(-7)
from 7 to 1 & 9 to 15
first term can be from 1 to 7 & 9 to 15
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