Question

3. If 7 times the 7th term of an AP is equal to 11 times its 11th term, find its 18th term.

Answer 1

Solution :..

7th term of A. P. = a7 = a + (7 - 1) d

a 7 = a + 6 d -----> ( i )

11th term of the A. P., a 11 = a + ( 11 - 1 ) d

a11 = a + 10 d -----> ( ii )

According to the question,

7 * a 7 = 11 * a 11

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

7a + 42 d = 11 a + 110 d

42 d - 110 d = 11 a - 7a

4a = - 68 d

a = - 68 d / 4

a = - 17 d

=> 18th term of the A. P., a 18 = a + ( n - 1 ) d

a 18 = a + 17 d

a 18 = - 17 d + 17 d [ Putting value of a = - 17 d ]

a 18 = 0.

=> a 18 = 0.