Why is it easier to count on to add if you start with the greater addend

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

3 years ago

How do i solve using the substitution method? x+y=-1 y=-2x

leonid [27]

Answer:

$(1, -2)$

Step-by-step explanation:

Step 1: Set the second equation into the first

$x + (-2x) = -1$

$x - 2x = -1$

$-x / -1 = -1 / -1$

$x = 1$

Step 2: Solve the second equation

$y = -2(1)$

$y = -2$

Answer: $(1, -2)$

4 0

3 years ago

Read 2 more answers

A ski patrol unit has seven members available for duty, and two of them are to be sent to rescue an injured skier. In how many w

ikadub [295]

Answer:

21

Step-by-step explanation:

7C2 = 21

6 0

3 years ago

What is the sum of the interior angles of a pentagon

Juliette [100K]

3 $\pi$ radians

8 0

3 years ago

Convert the equation from intercept form to standard form. y= 3(x-1)(x-4)

Sergeu [11.5K]

Answer:

I think the answer is y = 3x + 12.

Step-by-step explanation:

y = 3 (x - 1) (x - 4)

y = 3x -3 (x - 4)

y = 3x + 12

7 0

3 years ago