Question

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

Answer 1

Answer:

Given :  

10 times the 10th term of an A.P is equal to 15 times the 15 term

10a10 = 15a15

10[a + (10 – 1)d] = 15[a + (15 – 1)d]

[an = a + (n - 1)d]

10[a + 9d] = 15[a + 14d]

2[a + 9d] = 3[a + 14d]

[Dividing by 5 on both sides]

2a + 18d = 3a + 42d

2a - 3a = 42d - 18d

- a = 42d – 18d

-a = 24d

a = - 24d …………..(1)

 

25th term :  

an = a + (n - 1)d

a25 = a + (25 - 1)d

a25 = a + 24d

a25 = -24d + 24d

[From eq 1]  

a25 = 0 (zero)

25th term of an A.P is zero.

Hence, Proved  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Heya!

Here is ur answer...

Given,

10 times of the 10th term of an AP is equal to 15 times of the 15th term

As we know,

10th term = a10 = a+9d

15th term = a15 = a+14d

Therefore,

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

10a+90d = 15a+210d

15a-10a +210d -90d = 0

5a+120d = 0

a+24d = 0

Therefore,

a25 = 0

Hence proved!

Hope it helps..