Question

If 7 times the 7th term of an A.P. is equal to 11 times the 11th term.Find 18th term of A.P.?

Answer 1

7th term = (a+6d)                         11th term = (a+10d)
(a+6d)7  since 7th term of the ap is 7 times               and the same for 11th term
(a+6d)7=(A+10d)11                   (given)
7a + 42d =11a +110d                       (on solving)
7a - 11a = 110d - 42d
-4a = -68d
a= -17d


we know 18th term = (a+17d)................................. (i)
now we substitute the value of a in (i) 
which emplies,
                       -17d + 17d
                     = 0
hence prove..