Four numbers are in A.P. If sum of numbers is 50 and larger number is

1.	Four numbers are in A.P. If sum of numbers is 50 and larger number is 4 times the smaller number, then find the number.
Answer» Let four numbers in A.P. are a, a + d, a + 2d, a + 3d According to question a + (a + d) + (a + 2d) + (a + 3d) = 50 ⇒ 4a + 6d = 50 ⇒ 2(2a + 3d) = 50 ⇒ 2a + 3d = 25 …..(i) If larger number is 4 times the smaller number, then equation will be as follow, a + 3d = 4 x a ⇒ a + 3d = 4a ⇒ 3d = 3a ⇒ d = a …(ii) from equation (i) and (ii) 2a + 3a = 25 [∴ d = a] a = 25 a = 5 ∴ d = 5 [∵ eqⁿ(ii)] ∴ Numbers a = 5 a + d = 5 + 5 = 10 a + 2d = 5 + 2 × 5 = 15 a + 3d = 5 + 3 × 5 = 20 Hence, four numbers are 5, 10, 15, and 20

Four numbers are in A.P. If sum of numbers is 50 and larger number is 4 times the smaller number, then find the number.

Answer»

Let four numbers in A.P. are

a, a + d, a + 2d, a + 3d

According to question

a + (a + d) + (a + 2d) + (a + 3d) = 50

⇒ 4a + 6d = 50

⇒ 2(2a + 3d) = 50

⇒ 2a + 3d = 25 …..(i)

If larger number is 4 times the smaller number, then equation will be as follow,

a + 3d = 4 x a

⇒ a + 3d = 4a

⇒ 3d = 3a

⇒ d = a …(ii)

from equation (i) and (ii)

2a + 3a = 25 [∴ d = a]

a = 25

a = 5

∴ d = 5 [∵ eqⁿ(ii)]

∴ Numbers a = 5

a + d = 5 + 5 = 10

a + 2d = 5 + 2 × 5 = 15

a + 3d = 5 + 3 × 5 = 20

Hence, four numbers are 5, 10, 15, and 20