All categories

3 years ago

Which of the following sequences of numbers are arithmetic sequences?

Mathematics

2 answers:

serg [7]3 years ago

5 0

Hello,

A:no
B:no
C,D,E :yes

All you have to do : is the difference of next term and the term must be constant.

Zigmanuir [339]3 years ago

4 0

Answer:

C), D) and E)

Step-by-step explanation:

First let's see what an arithmetic sequence is.

A arithmetic sequence is series of numbers where the difference between the successive terms must be a constant.

For example,

2, 4, 6, 8, 10.....

If you find the difference between the successive terms, it will be the same constant.

4 -2 = 2

6 -4 = 2

8 -6 = 2

This is called arithmetic sequence.

A and B are not the arithmetic sequence. The different is not the same constant.

C) 345, 346, 347, 348, 349....

Difference = 1 between the two successive terms.

So it is an arithmetic sequence.

D) 54, 71, 88, 105, 122...

Difference = 71 - 54 = 17

88 - 71 = 17

So it is an arithmetic sequence.

E) -3, -10, -17, -24, -31...

Difference = -10 -(-3) = -10 + 3 = -7

Difference of -10 and -17 is -17 -(-10) = -17 +10 = -7

So it is an arithmetic sequence.

Answer: C), D) and E)

You might be interested in

PLEASE HELP I REALLY DONT UNDERSTAND HOW TO DO THESE QUESTIONS!!!!! THANK YOU I APPRECIATE YOU!!!!

liraira [26]

Answer:

a) $42,580

b) $43,900

Step-by-step explanation:

Recall, "mode" refers to the value which occurs most frequently.

In this case, the question says that there are 2 modes,

this means $34,000 and $50,500 both share the spot for the most frequently appearing salary.

because there are only 5 employees (and hence 5 salaries), the only possible way that there are two modes is if there are two of each mode, leaving only the last salary unknown.

i.e if we list the 5 salaries (in no particular order)

$34,000 $34,000 $50,500 $50,500 $ x

where x is the 5th unknown salary.

Given that the mean is $42,100

Then (34,000 + 34,000 + 50,500 + 50,500 + x) / 5 = 42,100

solving for x gives x = $41,500

Now we know all the values, we can rearrange them in increasing value:

$34,000 $34,000 $41,500 $50,500 $50,500

from this, we can see that the median salary is $41,500

Given that the median salary gets a $2400 raise,

the new median salary = $41,500 + $2400 = $43,900 (Ans for part b)

new mean salary,

= ($34,000 + $34,000 + $43,900 + $50,500 + $50,500 ) / 5

= $42,580 (answer for part a)

4 0

3 years ago

Can I get help solving this graph please?

Daniel [21]

see the attached figure with the letters

1) find m(x) in the interval A,B
A (0,100) B(50,40) -------------- > p=(y2-y1(/(x2-x1)=(40-100)/(50-0)=-6/5
m=px+b---------- > 100=(-6/5)*0 +b------------- > b=100
mAB=(-6/5)x+100

2) find m(x) in the interval B,C
B(50,40) C(100,100) -------------- > p=(y2-y1(/(x2-x1)=(100-40)/(100-50)=6/5
m=px+b---------- > 40=(6/5)*50 +b------------- > b=-20
mBC=(6/5)x-20

3) find n(x) in the interval A,B
A (0,0) B(50,60) -------------- > p=(y2-y1(/(x2-x1)=(60)/(50)=6/5
n=px+b---------- > 0=(6/5)*0 +b------------- > b=0
nAB=(6/5)x

4) find n(x) in the interval B,C
B(50,60) C(100,90) -------------- > p=(y2-y1(/(x2-x1)=(90-60)/(100-50)=3/5
n=px+b---------- > 60=(3/5)*50 +b------------- > b=30
nBC=(3/5)x+30

5) find h(x) = n(m(x)) in the interval A,B
mAB=(-6/5)x+100
nAB=(6/5)x
then
n(m(x))=(6/5)*[(-6/5)x+100]=(-36/25)x+120
h(x)=(-36/25)x+120
find <span>h'(x)
</span>h'(x)=-36/25=-1.44

6) find h(x) = n(m(x)) in the interval B,C
mBC=(6/5)x-20
nBC=(3/5)x+30
then
n(m(x))=(3/5)*[(6/5)x-20]+30 =(18/25)x-12+30=(18/25)x+18
h(x)=(18/25)x+18
find h'(x)
h'(x)=18/25=0.72

for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72

<span> h'(x) = 1.44 ------------ > not exist</span>