Question

find 4 no.s in AP whose sum is 50 and in which the greatest no. is 4 times the least

Answer 1

Here is your answer....
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Let the 4 terms in the A.P be : a-3d, a-d,a+d,a+3d
Now, accordind to the first condition,
(a-3d)+(a-d)+(a+d)+(a+3d)=50
a-d+a-3d+a+d+a+3d=50
a+a+a+a=50
4a=50
a=50/4
a=12.5
According to the second condition,
4(a-3d)=a+3d
4a-12d=a+3d
4a-a=12d+3d
3a=15d
a=5d
12.5=5d.....................(substituting the value of a)
d=12.5/5
d=2.5
∴a=12.5 and d=2.5
The four terms are as follows,
a-3d=12.5-3(2.5)=12.5-7.5=5.0
a-d=12.5-2.5=10.0
a+d=12.5=2.5=15.0
a+3d=12.5+3(2.5)=12.5+7.5=20.0
The four terms are: 5, 10, 15, 20
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DONE!
Hope it helps!