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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

Which pair of fractions and mixed numbers have a common denominator of 20?

Tomtit [17]

Answer:

D 3 3/4 and 7/10

Step-by-step explanation:

A) 2 3/8 and 3/4

4 goes into 20 evenly but 8 does not

NO

B) 1 5/6 and 2/5

5 goes into 20 evenly but 6 does not

NO

C) 4 1/3 and 1/4

4 goes into 20 evenly but 3 does not

NO

D) 3 3/4 and 7/10

4 goes into 20 evenly and 10 goes into 20 evenly

YES 3 3/4 = 3 15/20 and 7/10 = 14/20

8 0

3 years ago

How much time will it take for the plane to land?

serious [3.7K]

Answer:

Again assuming we're cleared for immediate take off, it takes around 20 minutes to climb to cruise altitude, at an average ground speed of (say) 200 knots. This means we've covered about 70 miles, which the cruising aircraft would have covered in just over 10 minutes. So this final phase has cost us another 10 minutes

7 0

2 years ago

Astronomers measure large distance in light years one light year is the distance that light can travel in one year, or approxima

crimeas [40]

Answer:

78,792,000,000,000 miles

Step-by-step explanation:

(5.88 * 10^12) * 13.4 = 78,792,000,000,000

7 0

2 years ago

Read 2 more answers

Carmen cut a 12 meter piece of cloth into three pieces. The first two pieces were each

astraxan [27]

Answer:

6 Meters long

Step-by-step explanation:

3+3=6

12-6=6

8 0

2 years ago