Question

Use n to represent the position of a term in the sequence where n =1 for the first term 0, 1, 2, 3, ...

Answer 1

`a_(n) = a_(1) + (n-1)`this is the required representation for showing the position of a term in the sequence.

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.

`a_(1) = \textrm{represent the first term in the sequence.} = 0`

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

`a_(n) = a_(1) + (n-1)* d`

`a_(n) = a_(1) + (n-1)`

If we require first term put n = 1

`a_(1) = a_(1) + (1-1)`

`a_(1) = 0`

If we require second term put n = 2

`a_(2) = a_(1) + (2-1)`

`a_(2) = 0 + 1`

`a_(2) = 1`

If we require third term put n = 3

`a_(3) = a_(1) + (3-1)`

`a_(3) = 0 + 2`

`a_(3) = 2`

and so on.......