Question

the 4 term of an ap is zero prove that the 25 term AP is the AP is there time it's 11 term

Answer 1

For the 4th term
a+3d = 0
a = -3d (1)

For the 11th term
a11 = a + 10d
Now by Substituting (1) ,
a11 = -3d + 10d
a11 = 7d (2)

For the 25th term
a25 = a + 24d
Now by Substituting (1) ,
a25 = -3d + 24d
a25 = 21d
a25 = 3 * (7d)
Now by Substituting (2) ,
a25 = 3 * a11

Answer 2

What's a ?

=> a is the first term of the AP .

What's d ?

=> d is the common difference between the terms.

AP stands for Arithmetic Progressions.

How to write an Arithmetic Progression with the help of first term 'a' and common difference 'd'?

=> Arithmetic Progression -

a , a+d , a+2d , a+3d , a+4d ...

What is an Arithmetic Progression?

A sequence whose terms increase or decrease by fix number is called arithmetic progression.

And this fix number is - 'd' aka common difference between the terms.