Question

If nine times ninth term is equal to the fifteen times fifteenth term, show that six times twenty fourth term is zero.​

Answer 1

$\mathcal{Answer}$

9t9 = 15t15

9(a + 8d) = 15(a + 14d)

9a + 72d = 15a + 210 d

15a - 9a + 210d - 72d = 0

6a + 138d = 0

6(a + 23d) = 0

a + 23d = 0

t24 = 0

Hence proved.

Answer 2

Answer ->

Let the first term be x and denominator be the common difference.

Nine times the 9th term = 9 ( a + [ 9 -1 ]d)

9 ( a + 8d )

15 time the 15th term

= 15 ( a + 14d)

Now they both are equal

9 ( a + 8d ) = 15 ( a + 14d )

9a + 72d = 15a + 210d

6a + 138d = 0

6 ( a + 23d ) = 0

a + 23d = 0

Hence, proved

Thanks!! ☺