Question

if 7 times the 7th term of an ap is equal to 8 times the 8th term show that 15th term of the ap is zero

Answer 1

Hi Mate!!!

7th term of A.p is = ( a + 6d )

8th term of A.p is = ( a + 7d )

and

15th term of A.p is = ( a + 14d ) ..... equation 1

where a is ist term and d is common difference


According to the question.

7 ( 7th term of A.p ) = 8 ( 8th term of A.p)

7 ( a + 6d ) = 8 ( a + 7d )

a = -14d


Now, put value of a in equation 1 we get

15th term = - 14d + 14d

15th term = 0


Have a nice day

Answer 2

OR
$7t7 = 8t8 \\ 7(a + 6d) = 8(a + 7d) \\ 7a + 42d = 8a + 56d \\ 7a - 8a = 56d - 42d \\ - a = 14d \\ now. \\ t15 = a + (15 - 1)d \\ \: \: \: \: \: \: \: = a + 14d \\ \: \: \: \: \: \: \: = a + ( - a) \\ \: \: \: \: \: \: \: = a - a \\ \: \: \: \: \: \: \: = 0 \\ t15 = 0 \\ hence \: proof$