Question

if the 2nd term of an AP is 13 and the fifth term is 25, what is the 9th term?

Answer 1

let first term be 'a' nd common difference be 'd'
 a+d= 13   ---------------- (i)
a+4d= 25  ---------------- (ii)
on solving both we get
  d = 4 nd a = 9
 therefore, 9th term  is
 a+8d = 9 + 8*4 = 9+32 = 41

Answer 2

We can write the terms of an A.P. (if the first term is taken as "a" and the common difference as "d") :
First term : a 
Second term : a+d
Third term : a+2d 
.............................
As per the question:
 Second term = 13
 a + d = 13   ---(i)

and

fifth term = 25
a + 4d = 25 -----(ii)

subtracting (i) from (ii):
       a + 4d - a - d = 25 - 13
                       3d = 12
                         d = 4
Now, using this in (i):
           a + (4) = 13
                    a = 9

So, we can find the ninth term easily.
                 Ninth term = a + 8d
                                   = 9 + 8(4)
                                   = 41