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Question

Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.


Solution

Let the four numbers in A.P. be
Sum = 50
a3d,ad,a+d,a+3d(a3d)+(a+d)+(a+d)+(a+3d)=504a=50
a=252(i)
and
(a+3d)=4(a3d)25+6d2=5012d30d=75d=2510=52(ii)
The terms are as follows
(2523×52),(25252),(252+52),(252+3×52)
=5,10,15,20

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