Question

Find 4 numbers in an increasing ap whose sum is 50 and the greatest number is 4 time the least

Answer 1

take the numbers as a-3d a-d a+d , a+3d and then solve

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

sorry i cant solve the whole question

but hope that helps

Answer 2

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.