All categories

3 years ago

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

Mathematics

1 answer:

joja [24]3 years ago

3 0

Options:

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

Answer:

C. –10, –7.5, –5, –2.5, …

Step-by-step explanation:

Given

f(n+1) = f(n) + 2.5 where n ≥ 1

Required

Which sequence partially defines the function

This question will be solved using trial by error method (we'll check out all given options)

We'll take f(1) as the first time of each sequence because n >= 1.

2.5, 6.25, 15.625, 39.0625, …

f(1) = 2.5

f(n+1) = f(n) + 2.5

So, when n = 1

f(1 + 1) = f(1) + 2.5

f(2) = 2.5 + 2.5 = 5

This doesn't define the sequence

2.5, 5, 10, 20

f(1) = 2.5

So, when n = 1

f(1 + 1) = f(1) + 2.5

f(2) = 2.5 + 2.5 = 5

When n = 2

f(2 + 1) = f(2) + 2.5

f(3) = 5 + 2.5

f(3) = 7.5

This also doesn't define the sequence

-10, -7.5, -5, -2.5, …

f(1) = -10

So, when n = 1

f(1 + 1) = f(1) + 2.5

f(2) = -10 + 2.5 = -7.5

When n = 2

f(2 + 1) = f(2) + 2.5

f(3) = -7.5 + 2.5 = -5

When n = 3

f(3 + 1) = f(3) + 2.5

f(4) = -5 + 2.5 = -2.5

This defines the function; so, there's no need to check D

You might be interested in

Steve took a 300 mile business trip and decided to travel by car. He drove the speed limit for half the trip until an accident o

svetoff [14.1K]

Answer:

He traveled for 2.5 hrs at 54 mi/hr

He traveled for 3 hrs at 61 mi/hr

------------------------------

check:

(1) +d+=+54t+

(1) +d+=+54%2A2.5+

(1) +d+=+135+ mi

3 0

3 years ago

Someone help please

astraxan [27]

The arc length (s) is given in terms of the radius by
s = rθ
10 cm = r*(29/180*π) radians
r = (10 cm)*(180/(29π)) ≈ 19.757 cm

d = 2r ≈ 2*19.757 cm ≈ 39.51 cm . . . . . . . matches selection G

8 0

4 years ago

The sum of 9 and three times a number is 21. What is the number?<br> equation: <br><br><br> n =

Yakvenalex [24]

To solve equations like this we need to do inverse operations.

First we need to build an equation: 9+3x=21

We pass the nine to the other side, subtracting the 9 to 21, that leaves us with 3x=12

After that we just divide 12 by 3, wich gives us x=4, or, as it says in the question: n=4

Now let's double check:

N=4, since 3*4=12 and 12+9=21

Hope it is helpful :)

8 0

3 years ago

How do you answer (2a)³ ?

s2008m [1.1K]

$(2a)^{3}$
Can be rewritten as;
2a*2a*2a
= $8a^{3}$

5 0

3 years ago

Read 2 more answers

A simple random sample of size equals 49 is obtained from a population with mu equals 88 and sigma equals 14. (a) Describe the

Gnoma [55]

Answer:

a) $\bar X \sim N(88,\frac{14}{\sqrt{49}}=2)$

b) $P(\bar X >91.2)=1-P(\bar X$

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$