Question

9. If the 5th term of an A.P. is zero, then show that the 25th term is twice the 15th term.
Ans. ​

Answer 1

Given

we have given 5th term of ap is zero

To show

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

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

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

Answer 2

refer to the attachment

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