# Find the four no,s in a.p whose sum is 50 and in which the greatest no. is 4 times the least

2
by sandy661

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by sandy661

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then a-3d+a-d+a+d+a+3d=50

4a=50

a=25/2

but a+3d=4(a-3d)

a+3d=4a-12d

3a=15d

a=5d

25/2=5d

d=5/2

so the 4 no's are

a-3d=25/2-15/2=10/2=5

a-d=25/2-5/2=20/2=10

a+d= 25/2+5/2=15

a+3d= 25/2+15/2=20

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Let the 4 number be a - 3d , a - d , a + d , a +3 d

then a - 3d +a - d + a + d + a + 3d=50

4a=50

a=25/2

but a + 3d = 4(a-3d)

a + 3d = 4a - 12d

3a=15d

a=5d

25/2=5d

d=5/2

so the 4 no's are

a-3d=25/2-15/2=10/2=5

a-d=25/2-5/2=20/2=10

a+d= 25/2+5/2=15

a+3d= 25/2+15/2=20

then a - 3d +a - d + a + d + a + 3d=50

4a=50

a=25/2

but a + 3d = 4(a-3d)

a + 3d = 4a - 12d

3a=15d

a=5d

25/2=5d

d=5/2

so the 4 no's are

a-3d=25/2-15/2=10/2=5

a-d=25/2-5/2=20/2=10

a+d= 25/2+5/2=15

a+3d= 25/2+15/2=20