Question

In an A.P., t7=20 and t18=42. then what is the common difference?

Answer 1

t7 = 20
t18 = 42
                        t7 = a + (n -  1) d
                       20 = a + 6d           .......................(1)
and,
                      t18 = a + (n - 1) d
                      42  = a + 17d           .......................(2)

from (1) and (2) we get that  
                                  a = 8 and d = 2  

Answer 2

t7=20 and t18= 42
t7= a+6d=20
   =>a=20-6d  -(i)
t18=a+17d=42
     =>20-6d+17d=42    -{using (i)}
     =>20+11d=42
     =>11d=42-20
     =>11d=22
     =>d=2

Therefore, common difference is 2.