Find a30 -a20 for the AP a, a+d, a+2d, a+3d........

an=a+(n-1)d so a30=a+(30-1)d=a+29d

Similarly a20=a+19d
so their difference is; a+29d-(a+19d)=a+29d-a-19d=10d

a30

To find a30 - a20 for an arithmetic progression (AP) with common difference d, we need to find the values of a30 and a20 first.

The formula to find the nth term of an AP is given by:
an = a + (n-1)d

Using this formula, we can find a30 and a20.

a30 = a + (30-1)d
a20 = a + (20-1)d

Next, we need to find the difference between these two terms:

a30 - a20 = (a + (30-1)d) - (a + (20-1)d)
= (a + 29d) - (a + 19d)
= a + 29d - a - 19d
= 29d - 19d
= 10d

Hence, the value of a30 - a20 for the given AP is 10d.

To find a formula for the n-th term of an arithmetic progression (AP), we can use the formula:

an = a + (n-1)d,

where "a" is the first term, "n" is the position of the term in the sequence, and "d" is the common difference.

Given that the AP is a, a+d, a+2d, a+3d, ...

To find a30, substitute n=30:

a30 = a + (30-1)d = a + 29d.

Similarly, to find a20, substitute n=20:

a20 = a + (20-1)d = a + 19d.

Now, to find a30 - a20:

(a30) - (a20) = (a + 29d) - (a + 19d).

Simplifying further:

a30 - a20 = a + 29d - a - 19d.

The "a" term cancels out, leaving us with:

a30 - a20 = 10d.

Therefore, a30 - a20 = 10d, which means the difference between the 30th term and the 20th term in the arithmetic progression is 10 times the common difference (d).