If 7 times the 7th term of an A.P. is equal to 11 times the 11th term,show that 18th term of A.P. is 0.

Let 1st term of AP be 'a',

Let the common difference be 'd',

So,as per question, 7 x 7th term = 11 x 11th term

or, 7 [a+6d] = 11 [a+10d]

or, 7a+42d = 11a +110d

or, 4a + 68d = 0

or, a + 17d = 0 .......(1)

Now, 18th term = a+17d

or, t_{18} = 0 { From (1)}

**Proved**