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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

Respuesta :

sqdancefan

Answer:

B. x/13

Step-by-step 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.

kudzordzifrancis
ANSWER

B.

[tex] \frac{x}{13} [/tex]

EXPLANATION

The given sequence is

[tex] \frac{1}{13} , \frac{2}{13} , \frac{3}{13} , \frac{4}{13} ,...[/tex]

There is a constant difference of

[tex]d = \frac{4}{13} - \frac{3}{13} = \frac{3}{13} - \frac{2}{13} = \frac{2}{13} - \frac{1}{13} = \frac{1}{13} [/tex]


This implies that the sequence is an arithmetic progression.

The general arithmetic sequence is of the form:

[tex]U_x=a_1+(x-1)d
[/tex]

The first term of this sequence is

[tex]a_1= \frac{1}{13} [/tex]

We substitute the given values to obtain,

[tex]U_x= \frac{1}{13} +(x-1) \times \frac{1}{13}
[/tex]

We expand the bracket to obtain,

[tex]U_x= \frac{1}{13} + \frac{x}{13} - \frac{1}{13} [/tex]

This simplifies to,

[tex]U_x= \frac{x}{13}
[/tex]

The correct answer is B.

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