How to find nth term of Arithmetic Sequence?
Suppose, we are given an Arithmetic sequence:
, how can we find 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 sequence.}
We will represent the nth term using
.
is also called general term of arithmetic sequence.
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 sequence 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 sequence.
Ember Shahad says
why do we subtract n by 1?