Question

Write an expression to describe the sequence below. 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

The expression  $a_n = a_1 + (n-1)d$  can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.

The given sequence is 0, 1, 2, 3, .......

We will use n to represent the position of a term such that n = 1 for the first term, n = 2 for the second term, n= 3 for the third term, and n = 3 for the third term in the given sequence.

What is an arithmetic sequence?

It is a sequence of numbers where the difference between the consecutive terms is same.

The nth term in an arithmetic sequence is given by:

$a_n = a_1 + (n-1)d\\where~a_1=first~term~and ~d=common~difference$.

The given sequence 0, 1, 2, 3, ...... is an arithmetic sequence.

d = 1 - 0 = 1

d = 2 - 1 = 1

d = 3 - 2 = 1

The difference between the consecutive terms is the same.

In the sequence 0, 1, 2, 3, ......

$a_1 = 0, a_2=1, a_2=2, a_3=3, and~so~on.$

If we use the arithmetic sequence nth term formula

we get,

$a_1=0+(1-1)1=0\\a_2=0+(2-1)1=1\\a_3=0+(3-1)1=2\\a_4=0+(4-1)1=3\\...\\...\\...$

Thus the expression  $a_n = a_1 + (n-1)d$ can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.

Or we can simply say  $a_n=n-1$  since  $a_1=0 ~and~ d=1$.

Learn more about arithmetic sequence here:

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