Arthimatic progression

nth Term of an AP

• a, a + d, a + 2d, a + 3d, a + 4d, . . .is an AP. where a is the first term, and d is the common difference.
• If we wanted to write down the n-th term, we would have a + (n − 1)d ,

Let’s see an example

EXAMPLE 1: Let a=2, d=2, n=12,find An An=a+(n-1)d

=2+(12-1)2

=2+(11)2

=2+22

Therefore, An=24

Hence solved.

nth Term of an AP

Example-2: Write down the first five terms of the AP with first term 8 and common difference 7.

Ans: 8,15,22,29,36

Example-3: Write down the first five terms of the AP with first term 2 and common difference −5.

Ans: 2, -3, -8,-13,-18

nth Term of an AP

Example 4: What is the common difference of the AP 11, −1, −13, −25, . . . ?

Ans: common difference = -1-11

=-13-(-1)

=-12