All categories

2 years ago

Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

Mathematics

2 answers:

NNADVOKAT [17]2 years ago

7 0

Answer: The correct option is

(B) $f(n+1)=f(n)-5.$

Step-by-step explanation: We are given to select the correct recursive formula that can be used to generate the following sequence :

$f(1)=6,n\geq1,\\\\6,1,-4,-9,-14,...$

Let f(n) denote the nth term of the given sequence. Then, we note that

$f(1)=6,\\\\f(2)=1=6-5=f(1)-5,\\\\f(3)=-4=1-5=f(2)-5,\\\\f(4)=-9=-4-5=f(3)-5,\\\\f(5)=-14=-9-5=f(4)-5,\cdots$

Therefore, the recursive formula can be written as :

$f(n+1)=f(n)-5.$

Thus, the required recursive formula is $f(n+1)=f(n)-5.$

Option (B) is CORRECT.

Nat2105 [25]2 years ago

4 0

Answer:

Step-by-step explanation:

You might be interested in

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18 \pi18π18, pi

katrin [286]

The area of the cross section of the column is $18 \pi \ m^2$

Explanation:

Given that a building engineer analyzes a concrete column with a circular cross section.

Also, given that the circumference of the column is $18 \pi$ meters.

We need to determine the area of the cross section of the column.

The area of the cross section of the column can be determined using the formula,

$Area= \pi r^2$

First, we shall determine the value of the radius r.

Since, given that circumference is $18 \pi$ meters.

We have,

$2 \pi r=18 \pi$

$r=9$

Thus, the radius is $r=9$

Now, substituting the value $r=9$ in the formula $Area= \pi r^2$ , we get,

$Area = \pi (9)^2$

$Area = 81 \pi$

Thus, the area of the cross section of the column is $18 \pi \ m^2$

5 0

2 years ago

A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8o when staring at the top of the stat

Lyrx [107]

Answer:

$h=50.25\ ft$

Step-by-step explanation:

<u>Right Triangles </u>

In a right triangle, one of the internal angles is 90°. When this happens, there is always a longer side, called hypotenuse and two shorter sides, called legs. They relate to Pythagoras's theorem. The basic trigonometric relations also stand, including

$\displaystyle tan\alpha=\frac{a}{c}$

where a is the opposite leg to $\alpha$ and c is its adjacent led .

In our problem, we have a statue being looked by a person in such a way that the top of the statue forms an angle of 8° with the horizontal and the base of the statue forms an angle of 14° down. We also know the distance from the person to the statue is 50 ft. The situation is shown in the image below.

The height of the statue is h=a+b, where

$a=50tan8^o$

$b=50tan14^o$

Thus

$h=50tan8^o+50tan14^o$

$h=50(tan8^o+tan14^o)$

$\boxed{h=50.25\ ft}$

5 0

2 years ago

A rectangle has an area of 36 inches squared. Write an equation to show how the length (l) varies inversely the width (w).

Anastaziya [24]

Start with the first sentence, and the definition of the area of a rectangle:
l * w = 36

Rewrite the equation to get
l = 36 / w
or
w = 36 / l
Either one shows the inverse relationship between w and l.

Assuming the last part wants you to write an equation for an x-y graph, the equation would be
y = 36 / x

8 0

2 years ago

What is the time period of a loan for $2,500 at 12% exact interest if the amount of interest is $118.36? Round to the next highe

Marianna [84]

I believe it's 144 days.

Hope this helped!

5 0

2 years ago

Read 2 more answers

Based only on the information given in the diagram which congruence theorems or postulates could be givenas reasons why triangle

Evgesh-ka [11]

The answer is C, E, and F on Apex

3 0

2 years ago

Read 2 more answers