Question

Here's anyone can give my answer
then I will make it brain list....

Answer 1

Given = nth term of AP is in linear expression in n.

Let the two variables be a and b

So, nth term = an + b

=> an = an + b

For 1st term,

a1 = a + b

For 2nd term

a2 = 2a + b

For 3rd term

a3 = 3a + b

and so on....

Now, for a sequence of numbers to be an AP, there must be a common difference.

So, to satisfy the condition of AP,

a3 - a2 = a2 - a1 = d (common difference)

=> (3a + b) - (2a + b) = (2a + b) - (a + b)

=> a = a

Since d = a, this sequence or progression is an AP.