Find four numbers in A P , whose sum is 50 and in which the greatest number is 4 times - Maths - Arithmetic Progressions

Question

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

Titiksha Sharma · Accepted Answer

Let the AP be a ,a +d , a+2d , a+3d
Sum of AP = 50
therefore , a + a +d + a+2d + a+3d = 50
=> 4a + 6d = 50
2a + 3d = 25 (1)
Also given : the greatest no is 4 times the least
4(a) = a+3d
4a-a = 3d
a=d
putting a = d in (1) , we get
5d = 25
d=5
a=5 , as d=a
First four terms are : 5 , 10 ,15 , 20
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Find four numbers in A.P , whose sum is 50 and in which the greatest number is 4 times the least .