10. Four terms are in A.P. If sum of numbers is 50pand largest number

1.	10. Four terms are in A.P. If sum of numbers is 50pand largest number is four times the smallerone, then find the terms,
Answer» 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.

10. Four terms are in A.P. If sum of numbers is 50pand largest number is four times the smallerone, then find the terms,

Answer»

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.