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if divided 20 into four parts which are in ap such that product of the fourth is to the product of the second and third is the same as 2:3, then the smallest part is-
Let the numbers are a-3d,a-d,a+d and a+3d.
Now ratio to the foruth to the the product of the second and third is the same as 2:3,
a+3d = 2
(a+d)(a-3d) 3
Solve and you will get ans.
let the 4 terms of AP be : a-3d, a-d, a+d, a+3d.
then the sum of 4 terms is a-3d +a-d+a+d + a+3d = 4a
given that 4a= 20.
therefore, a=5.
now, again given that
(a+3d)/(a-d)(a+d) = 2/3
solving, we get d=-7, 5/2
now, least term is a-3d.
if d is+ve,then the value of term is least.
keeping the values for d and a, least term=-5/2
please approve my answer.
Let the four parts be (a-d), (a), (a+d), (a+2d).
Then, (a-d)+(a)+(a+d)+(a+2d)=20
2a+d=10
a=(10-d)/2
Now,
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