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. -1, 0, 1, 2, ...

Answer 1

Answer:

$a_n = -2 + n$ is an expression which describe the given sequence

Step-by-step explanation:

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.  

The general rule for the arithmetic sequence is given by;  

$a_n =a_1+(n-1)d$               ......[1]

where

$a_1$ represents  the first term

d represents the common difference

and n is the number of terms;

Given sequence: -1 , 0 , 1 , 2 , .....

This is an arithmetic sequence with common difference

Since,

0-(-1) = 1

1-0 =1

2-1 = 1 ....

Here, $a_1 = -1$

Substitute the value of $a_1 = -1$ , d =1 in [1] we get

$a_n = -1 +(n-1)(1)$

$a_n = -1 + n -1 = -2 +n$

Therefore,an expression which describe the given sequence is,  $a_n = -2 + n$