Question

if four numbers are in ap such that their sum is 50 and greatest number is 4 times the least number . find the numbers.

Answer 1

Let the 4 numbers are a , a + d , a + 2d , a + 3d.

Sum of 4 numbers AP = 50

a + a + d + a + 2d + a + 3d = 50

⇒ 4a + 6d = 50

⇒ 2a + 3d = 25 --------------(1)

Also given the greatest number is 4 times the least.

4(a) = a + 3d

4a - a = 3d

a = d

putting a = d in (1) , we obtain

5d = 25

d = 5

a = 5 but d = a.

∴ First four terms are 5 , 10 ,15 , 20

Answer 2

sum=50

 if the first term is a,
and the 4th term is t4 then

t4 = 4a
a+3d =4a
3d =3a
d= a

sum= n/2(2a+(n-1)d)
50= 4/2(2a+3a)              as a=d 
50=2*5a
a=5

that means a=d=5

the ap will be 5,10,15,20