**How to find nth term of Arithmetic Sequence?**

Suppose, we are given an Arithmetic sequence or Progression:

, how can we calculate its nth term.

Here, first term = a = 3

Common difference (d)=

We know that we add common difference to the any given term to get the next term.

For example, we add 3 to **first term (a)** to get second term = 3 + 3 = 6

We add 3 to the second term to get the third term = 6 + 3 = 9

We keep on repeating the process to find the next terms of the sequence.

Carefully watching the above procedure,

Second term = a +d = a + (2-1)d

Third term = (a +d) +d = a + 2d = a + (3-1)d

Fourth term = ( a + 2d) + d = a+ 3d = a + (4-1)d

Fifth term = ( a + 3d) +d = a+ 4d = a + (5-1)d

Similarly, nth term = a + (n-1)d

{It is general formula which we will use to find nth term of given arithmetic progression.}

We will represent the nth term using . is also called general term of AP.

Therefore,

Lets take an example now to clarify things, we are given a sequence

**Can you find 50th term of this sequence?**

Yes, it is simple. We will directly use the formula to find 50th term of this sequence. We just need to find values of different variables and put in the formula.

First term =

Common difference =

We need to find 50th term of the progression which means value of n is = 50

Putting all the values in the formula , we get

Therefore, 50th term of sequence is equal to .

Similarly, we can find nth term of any given Arithmetic Progression.