Which number is not a rational number?

Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8

vredina [299]

Question:

Consider the sequence of numbers: $\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

$f(n + 1) = f(n) + \frac{3}{8} .$

Explanation:

A sequence of numbers are

$\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Let us first change mixed fraction into improper fraction.

$\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}$

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

$\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}$

$\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}$

$\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}$

$\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}$

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding $\frac{3}{8}$ to the previous term.

Hence, the sequence is recursive and can be represented by the function $f(n + 1) = f(n) + \frac{3}{8} .$

3 0

2 years ago

a father and his son clean the house together in 2 hours. when the son works alone, it takes him an hour longer to clean than it

Marizza181 [45]

It takes the son one and half hours to clean the house. To find this you need the equations F+S=2 and F+1=S. (F=father and S=son) You take the F+1 and substitute it in for S in F+S to get F+(F+1)=2. Then you combined like factors, 2F+1=2, and simplify to get F=.5hr. After this you plug .5 in to F+1=S to get (.5)+1=S, meaning it takes the son 1.5 hour to clean the house.

7 0

3 years ago

The width of a soccer field should be 60% of its length. Write and simplify an expression for the perimeter of a soccer field wi

iogann1982 [59]

Answer:

here you go

Step-by-step explanation:

W = (0.6) L

P = 2 ( L + W )

P = 2 [ L + (0.6) L ]

P = 2 ( 1.6 L )

P = (3.2) L

P = (3.2) x

4 0

3 years ago

SOMEONE ANSWER ASAP ILL EVEN CASHAPP YOU A DOLLAR!!!

devlian [24]

Answer:

2/3

Step-by-step explanation:

-2 and 4 are 6 away

4 and 13 are 9 away

Thus it is 6/9 or 2/3

4 0

3 years ago

Read 2 more answers

What is 9 5/9-6 5/6 I seem to not get the right answer every time I try

gulaghasi [49]

If you would like to solve 9 5/9 - 6 5/6, you can calculate this using the following steps:

9 5/9 - 6 5/6 = 86/9 - 41/6 = 516/54 - 369/54 = (516 - 369) / 54 = 147/54 = 49/18 = 2 13/18

The correct result would be 2 13/18.

6 0

2 years ago

Read 2 more answers