Question

sorry this is a lot to ask for. but I need to study for my final! If someone could help me out it would be awesome! this is on sequence and series!

Answer 1

PLEASE HELP ME

Answer 2

1.) what are the first five terms of the sequence given by the formula An=5n+1?
A) 1,5,9,13,17
B) 6,11,16,21,26
C) 5,10,15,20,25
D) 5,6,7,8,9

2)write a recrusive definition for the sequence 11,8,5,2,...
A) a1=11,an=an-1-4
B) a1=11,an=an-1-3
C) a1=2, an=an-1-3
D) a1=2, an=an-1+3

3) write an explicit definition for the sequence -3,1,5,9,...
A) an=-3+4(n-1)
B) an=-3+4n
C) an=-3+ (n-1)
D) an= -3+4 (n+1)

4) suppose you drop a tennis ball from a height of 8 feet. after the ball hits the floor, it rebounds to 80% of its previous height. how high will the the ball rebound after its 3rd bounce?
A) 3.3 ft
B) 4.1 ft
C 5.1 ft
D) 1 ft

6) is the sequence arithmetic? if so identify the common difference. 14,21,42,77,...
A) yes; 7
B) yes;-7
C) yes; 14
D) no

7) what is the 12th term of the sequence 15,11,7,...
A) -29
B) -25
C)-21
D) -33

8) find the missing term of the arithmetic sequence 24, ___ , 36,...
A)34
B)30
C)42
D)20

10) what is the 10th term in the sequence 625,125,25,...
A) 1/3125
B) 1/625
C) 1/1,250
D) 1/15,625

11) what is a possible value for the missing term of the geometric sequence? 39, __ , 975,...
A)-44
B)-195
C)-5
D)-4,875

12) what is the sum of the finite arithmetic series? (-10) + 0+ 20+..... + 130
A) 900
B) 1,000
C) 950
D) 955

14) what is the sum of the arithmetic series? \[\sum_{t=1} (3t-4)\]
A)234
B)441
C)25.5
D)49

15) what is the sum of the first 10 terms of the sequence defined by an=3n-3?
A)132
B)138
C)27
D)135

16) what is the sum of the geometric series rounded to the nearest whole number? \[\sum_{x=0}^{15} 2(1/3)^x\]
A)2
B)3
C)4
D)1

18) does the infinite geometric series diverge or converge? Explain
A) diverge; it does not have a sum
B) converges; it does not have a sum
C) diverges; it has a sum
D) converges; it has a sum

Answer 3

Mai Gawd O_O

Answer 4

Let's start with number one, and we'll see how far we can get. So, number one states "1.) what are the first five terms of the sequence given by the formula An=5n+1?
A) 1,5,9,13,17
B) 6,11,16,21,26
C) 5,10,15,20,25
D) 5,6,7,8,9 "

Answer 5

Do you know how to find the terms, given n?

Answer 6

Well kinda. not quite! these are just all my question off my practice test I don't understand!

Answer 7

Ok, then think of each one like this: If n is equal to "x", then just put in whatever value x is for the "n" variable in "5n+1". Example: If n=1 (As your first one is), then put in one for n, getting "5(1)+1", which is the same as 6. Understand?

Answer 8

yea, that makes sence. do you always use 1 in replacement for x?

Answer 9

No, you replace n with whichever term you're trying to find. If you want to find the third term, for example, then just put a 3 in place of n.

Answer 10

oh! okay. I got it!

Answer 11

Then what's the answer for one?

Answer 12

B

Answer 13

Correct! Now, number two!

Answer 14

2)write a recrusive definition for the sequence 11,8,5,2,...
A) a1=11,an=an-1-4
B) a1=11,an=an-1-3
C) a1=2, an=an-1-3
D) a1=2, an=an-1+3

Answer 15

now, on this one can you help me get started I struggle on these.

Answer 16

I'm just thinking, one moment.

Answer 17

okay, thank you for even helping me! take your time.

Answer 18

Ok, firstly, what's the first term listed?

Answer 19

its 11

Answer 20

Yep, so that narrows the possible answers down to two, as saying "a1" is simply the first term. So, given this, it must be which of two answers? What or what?

Answer 21

its either A or B?

Answer 22

Yep. That being said, what's being added or subtracted from one term to get the next one?

Answer 23

its gotta be B?

Answer 24

Correct, as three is being subtracted, not four. Time for number three!

Answer 25

3) write an explicit definition for the sequence -3,1,5,9,...
A) an=-3+4(n-1)
B) an=-3+4n
C) an=-3+ (n-1)
D) an= -3+4 (n+1)

Answer 26

awesome! sounds good

Answer 27

The root formula for arithmetic equations will help greatly here. It is "a(n)=a1+d(n-1)", where a1 is the first term, d is how much is added or subtracted from a term to get the next one, and where n is the nth term in a series. So, we can ignore the a1 part, because all the answers have the same beginning parts. Ok?

Answer 28

ok, lets try this!

Answer 29

Now, what do we know is being added or subtracted from one term to the next?

Answer 30

adding 4

Answer 31

Yep! So which variable I just listed does that fit the description of?

Answer 32

would it be d?

Answer 33

You're close, but look at the last part of it. There's one difference between it and the root formula. What is it?

Answer 34

sorry! its A, I just noticed it.

Answer 35

There ya go :), correct! Make sure the sign is the same as the root formula before deciding the answer. Time for number 4!

Answer 36

4) suppose you drop a tennis ball from a height of 8 feet. after the ball hits the floor, it rebounds to 80% of its previous height. how high will the the ball rebound after its 3rd bounce?
A) 3.3 ft
B) 4.1 ft
C 5.1 ft
D) 1 ft

Answer 37

okay I will! perfect.

Answer 38

Essentially, we're finding 80%(80%(80% of 8 (feet)))). Understand where I got this?

Answer 39

yea. I do!

Answer 40

Good, then tell me, what is 80% of 80% of 80% of 8?

Answer 41

80% of 8 is 6?

Answer 42

No, how'd you get that? Make sure that you're doing ".8 x 8"

Answer 43

is the answer D?

Answer 44

Nope.

Answer 45

What is 80% of 8?

Answer 46

6

Answer 47

hm, I not sure how this one works

Answer 48

Put this into a calcuator: .8 x 8. What is the result?

Answer 49

.64

Answer 50

Yep. Now, multiply that by .8 again.

Answer 51

0.512

Answer 52

Oh, go back and do .8 x 8 again please. Make sure you note the placement of the decimal.

Answer 53

6.4?

Answer 54

Yeah, that's it. Now, multiply that by .8.

Answer 55

5.12

Answer 56

And once more please!

Answer 57

the answer is B!

Answer 58

Correct!

Answer 59

Now, problem 5!
6) is the sequence arithmetic? if so identify the common difference. 14,21,42,77,...
A) yes; 7
B) yes;-7
C) yes; 14
D) no

Answer 60

There is no number 5, so number 6 instead!

Answer 61

? @noseboy908

Answer 62

yea, just straight to number 6 hah

Answer 63

Now, for number 6, the key is that Arithmetic equations will always have the same "d". Thus, each term must be found by adding the same number each time to find the next one. (In all, if one number minus the previous number does NOT equal any other given number minus the previous number, then it's not arithmetic). So, what is added to the first term to get the second?

Answer 64

7 is added

Answer 65

A?

Answer 66

Don't be too hasty, let's check another two terms. Please tell me what is being added to the second term to get the second term.

Answer 67

21

Answer 68

Mhmm. Is that the same as what's being added to a1 to get a2?

Answer 69

no its not

Answer 70

Yep, so what do we then know about the series? Doesn't an arithmetic sequence require a constant number for "d"?

Answer 71

correct. its not an arithmetic sequence

Answer 72

There ya go. Time for number 7!

Answer 73

lol yup!

Answer 74

7) what is the 12th term of the sequence 15,11,7,...
A) -29
B) -25
C)-21
D) -33

Answer 75

Firstly, please restate the root formula for arithmetic equations that I previously gave you.

Answer 76

one sec. I think I can do this one, just let me know if im wrong.

Answer 77

Ok.

Answer 78

the answer would be A ?

Answer 79

Yep! At that, I'm afraid I must go, at least for now. But that's correct. I should return later to help if I'm still needed.

Answer 80

dang! around what time will you be back? I need your help! or the answers and I will work till I figure them out.

Answer 81

It's likely that I'll be back before 7 CST, ok?

Answer 82

so like 4 hours? I will message you then?

Answer 83

No, about two hours.

Answer 84

oh, okay. well then I will message you in 2 hours! thank you!

Answer 85

8) find the missing term of the arithmetic sequence 24, ___ , 36,...
A)34
B)30
C)42
D)20

Answer 86

Are you ready for more?

Answer 87

hey, im sorry! im back @noseboy908

Answer 88

Alright, then let's begin!

Answer 89

sweet. im ready, sorry I just sent you a messege

Answer 90

To start, please restate the root formula I gave you that is for arithmetic equations.

Answer 91

have the same "d". Thus, each term must be found by adding the same number each time to find the next one. (In all, if one number minus the previous number does NOT equal any other given number minus the previous number, then it's not arithmetic). is it this one?

Answer 92

Look again, I'm talking about a specific formula. It starts with "a(n)=a1..."

Answer 93

"a(n)=a1+d(n-1)"

Answer 94

Exactly! So, plug in what you know. What are you given, in terms of variables?

Answer 95

with 24 being the first variable?

Answer 96

Be specific: which variable?

Answer 97

n?

Answer 98

the answer is b correct?