Answer 1

A.P. a,a + d, a + 2d, a + 3d, ...

Here

First term (a) = a

Common difference of the A.P (d) = a + d -a = d

Now as we know

`a_n= a + (n - 1)d`

Here we find `a_30` and `a_20`

So for 30 th term

`a_30 = a + (30 - 1)d`

`= a + (29)d`

Also for 20 th term

`a_20 = a + (20 - 1)d`

= a - (19)d

So,

`a_30 - a_20 = (a + 29d) - (a + 19d)`

= a + 29d - a - 19d

= 10d

Therefore for the given A.P `a_30 - a_20 = 10d`