Question

four numbers are in AP the sum of the 3rd and 4th term is 3 times the sum of 1st two terms if 4th term is 14 then find the four numbers​

Answer 1

Let the numbers in AP be a , a + d , a + 2d and a + 3d .

ATQ .

a + 3d = 14

a = 14 - 3d ____(i)

Also,

a + 2d + ( 14 ) = 3 ( a + a + d )

a + 2d + 14 = 6a + 3d

5a + d = 14 ___(ii)

Putting value of a in (ii) equation :

5 ( 14 - 3d ) + d = 14

70 - 15d + d = 14

70 - 14d = 14

14d = 70 - 14

14d = 56

d = 4

Putting value of d in (i) equation :

a = 14 - 3(4)

a = 14 - 12 = 2

First term = a = 2

Second term = a + d = 6

Third term = a + 2d = 10

Fourth term = a + 3d = 14