Question

If 7 times 7th term of an A.P is equal to 11 times its 11th term then find its 18th term

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

Answer 2

given :-

7 ( a7 ) = 11 ( a11 )

7 ( a + 6d ) = 11 ( a + 10d )

7a + 42d = 11a + 110d

7a - 11a + 42d - 110d = 0

4a - 68d = 0

a - 17d = 0

a = 17d .... ( i )

To find 18th term

a18 = a + ( n - 1 )d

a18 = a + 17d

a18 = 17d + 17d

a18 = 34d