Question

Can someone help me with a few Questions?

Answer 1

That's why we're here.

Answer 2

Well yeah i know but not many people actually help me :(

Answer 3

What is your first question?

Answer 4

What is the first five terms of the sequence given by the formula an=6n+1?
A.) 7,13,19,25,31
B.) 1,7,13,19,25
C.) 6,12,18,24,30
D.) 13,19,25,31,37

Answer 5

is it
\[a_n=6n+1\]?

Answer 6

yeah

Answer 7

if so, start with \(n=1\) and get the first term
\[a_1=6\times 1+1=7\]

Answer 8

so then it would be A right?

Answer 9

the second term is
\[a_2=6\times 2+1=13\] but you could stop after \(a_1\) since only one choice begins with 7

Answer 10

yeah, A
very unusual, it is usually C

Answer 11

can you help me with a few others?

Answer 12

sure why not?

Answer 13

Use summation notation to write the series 2.2+6.6+11+.... for 5 terms

Answer 14

is it an arithmetic sequence? i.e. do you add one number to get to the next?

Answer 15

its an arithmetic sequence

Answer 16

if so, since \(6.6-2.4=4.4\) and also \(11-6.6=4.4\) the terms look like
\[2.2+6.6+11+15.4+19.8\]
you need to write this in sigma notation, you could use
\[\sum_{n=1}^52.2+(n-1)4.4\]

Answer 17

oops i meant \(6.6-2.2=4.4\) but the answer is still right

Answer 18

thanks i have just a couple more if you still dont mind

Answer 19

no problem
did you understand what i wrote?

Answer 20

Yeah i think so im not very good at Algebra
The choices that i had were
\[\sum_{n=1}^{5}(-4.4+6.6n)\]
\[\sum_{n=1}^{5}(-2.2+4.4n)\]
\[\sum_{n=0}^{4}(-2.2+8.8n)\]
\[\sum_{n=0}^{5}(-8.8+2.2n)\]

Answer 21

oh no sorry, go with the second one

Answer 22

the one with a \(4.4n\) in it

Answer 23

After you explained it i chose that one cause it was the only one with 4.4 instead of the negative

Answer 24

yeah, there are many different ways to write the same sum, so it can get confusing

Answer 25

Yeah but heres the next question
Does the infinite geometric series diverge or converge?Explain
2+6+18+54+...
A.) It diverges; it does not have a sum
B.) It converges; it does not have a sum
C.) It diverges; it has a sum
D.) It converges; it has a sum

Answer 26

the numbers are getting bigger, so it DIVERGES
that is a synonym for NOT having a sum

Answer 27

go with A

Answer 28

these two answers
B.) It converges; it does not have a sum C.) It diverges; it has a sum
make no sense no matter what the question is

Answer 29

Oh ok thanks i have one last muliple choice question to do then 3 that need to be explained in steps

Answer 30

go ahead and ask

Answer 31

Heres the multiple choice one
What is the 10th term of the sequence 625,125,25,....?
A.) 1/3125
B.) 1/125
C.) 1/1250
D.) 1/15625

Answer 32

looks like you are dividing by \(5\) each time

Answer 33

tenth term is
\[\frac{625}{5^9}\]

Answer 34

ok hold on a sec

Answer 35

can't use your calculator for this, you will get a decimal
look here
http://www.wolframalpha.com/input/?i=625%2F5^9

Answer 36

looks like it is
\[\frac{1}{3125}\]

Answer 37

i couldnt see the 9 on the fraction you had above that lol sorry

Answer 38

i can write \[\huge \text{bigger}\] if you like

Answer 39

No its fine lol

Answer 40

k got another? i will turn in to a pumpkin soon

Answer 41

yeah
The numbers of seats in the first 12 rows of high-school auditorium form an arithmetic sequence. The first row is 9 seats. The second row is 11 seats.
a.) Write a recursive form to represent the sequence
b.) Write an explicit formula to represent the sequence
c.) How many seat are in the 12th row?

Answer 42

recursion looks like \(a_1=9\) and \(a_n=a_{n-1}+2\) since the first one is 9 and you are adding two each time

Answer 43

explicit formula you have lots of choices.
easiest is probably \(a_n=9+2(n-1)\)

Answer 44

or you could say \(a_n=7+2n\) either way, it is the same

Answer 45

since \(a_n=7+2n\) the 12th row has
\[a_{12}=7+2\times1 2\] seats

Answer 46

so there would be 31 seats right?

Answer 47

yes

Answer 48

Kk
Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
a) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain
b) Write an explicit formula to represent the sequence.
c) Find the value of the computer at the beginning of the 6th year.

Answer 49

it is geometric because to decrease a number by \(10\%\) you multiply it by \(100\%-10\%=90\%=.9\) so each year the present value is multiplied by the same number (that makes it geometric) which in this case is \(.9\)

Answer 50

since each year it gets multiplied by \(.9\) you can write your sequence as
\[a_n=1250\times (.9)^{n-1}\]

Answer 51

oh, actually scratch that
use
\[a_n=1250\times (.9)^n\]

Answer 52

at the beginning of year 6, it will be worth \(1250\times (.9)^5\) i think

Answer 53

i got 738.1125 when i did it on the calculator

Answer 54

yeah me too
it is money so you might want to say \(\$738.11\)

Answer 55

that it?

Answer 56

One left

Answer 57

lol great

Answer 58

lol ok here it is

Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3+10+17+24+...
a) Use summation notation to write the series. Explain what the numbers in the summation represent in this situation and how you found the expression used in the summation.
b) Find the total number of beads in the necklace. Explain your method for finding the total number of beads.

Answer 59

ok this is an easier one
each row has 7 more than the previous one, starting at 3

Answer 60

you can use
\[\sum_{n=1}^{18}3+7(n-1)\] or
\[\sum_{n=1}^{18}-4+7n\]

Answer 61

if you use
\[\sum_{n=1}^{18}3+7(n-1)\] the number 3 represents the number of beads in the first row and \(7(n-1)\) means each successive row has 7 more beads

Answer 62

as for adding it up, there are lots of ways to do it
one is to use \(S=\frac{n(a_1+a_n)}{2}\) which in your case would be

Answer 63

\[\sum_{n=1}^{18}3+7(n-1)\]\[=\frac{18(3+122)}{2}\]

Answer 64

would that be 115 for the answer?

Answer 65

the 18 because there are 18 terms
the 3 because it is the first number
the 122 because it is the 18th number as \(3+7\times 17=122\)

Answer 66

oh no it is much bigger than that

Answer 67

oops

Answer 68

\[\frac{18(3+122)}{2}=9\times 125\]

Answer 69

that is all right?

Answer 70

so instead it would be 1125? thats what i got on calculator

Answer 71

that is what i get too

Answer 72

Ok Thank you so much for your help :)

Answer 73

yw
and now stop doing math and take a break

Answer 74

Lol ok i will

Answer 75

Also you should get more medals than what you got but i cant give anymore..your awesome