Find the A.P. whose 3rd term is 18 and 12th term is 72.

6, 12, 18....

In an AP ,

nth term

an = a1 + ( n - 1 )× d

18 = a1 + ( 3 - 1 )× d 

18 = a1 + 2d    ----(1)

72 = a1 + ( 12 - 1 )× d

72 = a1 + 11d     ----(2)

On subtracting equation 1 from equation 2 .

9d = 72 - 18 = 54

d = 6

18 = a1 + 2 × 6

a1 = 6

So, Series is

6 , 12 , 18 , 24 , 30 , 36, 42, 48 , 54, 60 , 66, 72

Ans :- 6 , 12 , 18 ................