Question

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

Answer 1

Hey user .

Here is your answer :-

We know that

tn = a + ( n - 1 )d

t7 = a + ( 7 - 1 )d

t7 = a + 6d

t11 = a + ( 11 - 1 )d

t11 = a + 10d

7 × t7 = 11 × t11

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

7a + 42d = 11a + 110d

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

4a + 68 = 0

a + 17d = 0

t18 = 0

So 18th term of the A.P. is 0.

Thank you.

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