The sum of three numbers in an AP is 18. If the product of the first and
the third term is 5 times
the common difference. Find the three numbers
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Answer:
the numbers are 2,6,10
Step-by-step explanation:
let the 1st term is a
common difference is d
so,2nd term is a+d
and,3 rd term is a+d+d=a+2d
according to question
a+(a+d)+(a+2d)=18
=> a+a+d+a+2d=18
=> 3a+3d=18
=> 3(a+d)=18
=> a+d=18/3=6
=> a=6-d
again,
a(a+2d)=5d
=> (6-d)(6-d+2d)=5d
=> (6-d)(6+d)=5d
=> 36-d^2=5d
=> d^2+5d-36=0
=> d^2+9d-4d-36=0
=> d(d+9)-4(d+9)=0
=> (d+9)(d-4)=0
=> d+9=0, d= -9
=> d-4=0, d=4
as the sum of the three numbers is positive,so d is positive.
here d=4
a=6-d=6-4=2
so the numbers are 2,2+4=6,6+4=10
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