Question

if 10times the 10th term of an A.p is equal to 15times terms of 15th term show that 25th term of A.p is zero

Answer 1

Hii here's the logic to the answer

Hope it helped

Answer 2

$\sf\huge\bold{\underline{\underline \red{{Solution}}}}$

$\green{{{{Given:-}}}}$

we have given 5th term of ap is zero

To show

we have to show that 25th term is twice the 15th term

since, we don't know the first term and common difference

So, let the first term be 'a'

common difference be 'd'

Identity to find nth term of an ap : an= a+(n-1)d

5th term = a+4d

since , 5th term is zero so,

a+4d=0-----(1)

25th term = a+24d

From equation 1

a= -4d

Now ,put a into 25th term

=> -4d+24d = 20d-----(2)

15th term = a+14d

=> -4d+14d

= 10d-----(3)

From equation 3 and 2

25th term = 2* 15th term

Hence,proved