Answer:
[tex]a_{n} = a_{1} + (n-1)[/tex]this is the required representation for showing the position of a term in the sequence.
Step-by-step explanation:
Given:
The sequence is as follow:
0, 1, 2, 3, .......
To Find:
The expression while using 'n' to represent the position of a term in the sequence where n = 1 for the first term 0, 1, 2, 3, ....
Solution:
n = to represent the position of the term in the sequence.
[tex]a_{1} = \textrm{represent the first term in the sequence.} = 0[/tex]
d = Common difference.,i.e difference between the consecutive term.
d = second term - first term.
or
d = third term - second term.
Here we have d = 1 - 0 = 1
or d = 2 - 1 = 1
So, the required expression is
[tex]a_{n} = a_{1} + (n-1)\times d[/tex]
[tex]a_{n} = a_{1} + (n-1)[/tex]
If we require first term put n = 1
[tex]a_{1} = a_{1} + (1-1)[/tex]
[tex]a_{1} = 0[/tex]
If we require second term put n = 2
[tex]a_{2} = a_{1} + (2-1)[/tex]
[tex]a_{2} = 0 + 1[/tex]
[tex]a_{2} = 1[/tex]
If we require third term put n = 3
[tex]a_{3} = a_{1} + (3-1)[/tex]
[tex]a_{3} = 0 + 2[/tex]
[tex]a_{3} = 2[/tex]
and so on.......
