Question

Which of the following is the algebraic expression that best describes the sequence 1/13, 2/13, 3/13, 4/13,...

A. 13x
B. x/13
C. x+1/13
D. 13/x

Answer 1

ANSWER

B.


`(x)/(13)`

EXPLANATION

The given sequence is


`(1)/(13) , (2)/(13) , (3)/(13) , (4)/(13) ,...`

There is a constant difference of


`d = (4)/(13) - (3)/(13) = (3)/(13) - (2)/(13) = (2)/(13) - (1)/(13) = (1)/(13)`


This implies that the sequence is an arithmetic progression.

The general arithmetic sequence is of the form:


`image`

The first term of this sequence is


`a_1= (1)/(13)`

We substitute the given values to obtain,


`image`

We expand the bracket to obtain,


`U_x= (1)/(13) + (x)/(13) - (1)/(13)`

This simplifies to,


`image`

The correct answer is B.

Answer 2

B. x/13

Explanation:

As x takes on integer values 1, 2, 3, 4, ..., the expression x/13 evaluates to ...

... 1/13, 2/13, 3/13, 4/13, ...

which matches the sequence in the problem statement.