Question

The values in the table represent a linear function. What is the common difference of the associated arithmetic sequence?

X Y
1 4
2 21
3 38
4 55
5 72
Choices
A. 17
B. 1
C. 19
D. 3

Answer 1

A bc the Y numbers increase by 17 every time X increases by 1

Answer 2

The common difference of the associated arithmetic sequence is:

Option: A

17

Explanation:

We know that the sequence is said to be arithmetic if each of the sequence is differ by the preceding term by a fix constant which is known as a common difference.

i.e. d is called a common difference of the sequence if
`a_n\ and\ a_(n+1)`

are the nth and (n+1)th term of the sequence then,

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

Here we have a table of values as:

X Y d

1 4

2 21 21-4=17

3 38 38-21=17

4 55 55-38=17

5 72 72-55=17

Hence, we get that the common difference is: 17