Question

Please Help!!

Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 4 + 1 + 6 + ... + 66

Answer 1

@SolomonZelman

Answer 2

Can you tell me the pattern (whether I know it or not)

Answer 3

n+5

Answer 4

i think

Answer 5

Yes, good. You add 5 each time.

Answer 6

66 is the last term, right ?

Answer 7

yes

Answer 8

\(\normalsize\color{blue}{ 66=-9 + 5(x) }\) x is `which number term is 66` in the sequence.
Makes sense so far ?

Answer 9

yeah, so i figure out what x is now?

Answer 10

yes, please:)

Answer 11

x=15

Answer 12

Yes, good !

Answer 13

So how many terms are there ?

Answer 14

15?

Answer 15

So we know what to put on top of the sigma, 15.

Answer 16

ok

Answer 17

\[\sum_{n=0}^{15}\left( -9+5n \right)\] is this what it will look like?

Answer 18

well, very good job, but then starting from index of 0, you get 16 terms 0,1,2,3,4,5 ...15

Answer 19

I would put\[\sum_{n=1}^{15}~~-9+5(n-1)\]

I like index of 1 better:) They make more sense to me.

Answer 20

but that isn't an answer choice >.<

Answer 21

thanks by the way, can you help me with a few more? @SolomonZelman

Answer 22

Yes, perhaps I can. I am not very good at math. Shoot ...!

Answer 23

Find the sum of the first 12 terms of the sequence. Show all work for full credit.

1, -4, -9, -14, . . .

Answer 24

pattern is? (you tell me)

Answer 25

-5

Answer 26

yes obviously you got this.
Now,
find the 12th term for me please.

Answer 27

is there a short cut to finding it??

Answer 28

if so, i don't know it TT^TT

Answer 29

\(\large\color{midnightblue}{ \rm a_n=a_1 +d(n-1) }\)

Answer 30

you saw this before I am sure...

Answer 31

ohhhhhhhhh yes that is very familiar

Answer 32

yes, so for 12th term, what would you do, using the \(\large\color{purple}{ \rm a_n=a_1 +d(n-1) }\)

Answer 33

\[a_{12}=1+5(12-1)\]??

Answer 34

12th term= 56??

Answer 35

yes !!!!

Answer 36

yay ^_^

Answer 37

Now, another formula....

\(\large\color{midnightblue}{ \rm S_n=\color{red}{\frac{1}{2}(a_1+a_n)}\times n }\)

Answer 38

Just the concept, it would make to say that the red part is the average term (in arithmetic sequence) right ?

Answer 39

it would make sense to say that the red, is the average term ?

Answer 40

yeah

Answer 41

So, can you find the sum ?

Answer 42

\(\large\color{midnightblue}{ \rm S_n=\color{red}{\frac{1}{2}(a_1+a_n)}\times n }\)

Answer 43

Hold on !

Answer 44

you found the 12th term incorrectly.
you subtract 5 to get to the next term,

a12 = a1 + (-5)(12-1) = a1 + (-55) = a1 - 55 = .... = -54

Answer 45

OH!!!! ok!!

Answer 46

now you can use the formula, \(\large\color{midnightblue}{ \rm S_n=\color{red}{\frac{1}{2}(a_1+a_n)}\times n }\)

\(\large\color{midnightblue}{ \rm S_{12}=\color{red}{\frac{1}{2}(1+(-54)~~)}\times 12 }\)

Answer 47

\[S_{12}=-318\]??

Answer 48

YES !

Answer 49

OH MY GOSH THANK YOU!!!! i love you so much >.<

Answer 50

can you help me with one more??...Please ??

Answer 51

Thank you, it's a pleasure to work with a smart person like you who can do the calculations (unlike so many other users on this website).

Answer 52

Yes, I think I can.

Answer 53

haha thanks >_< !!

Answer 54

A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?

Answer 55

sometimes i just need a boost in the right direction and nudges on the way XP

Answer 56

Ohh, I am sorry, I am not messing with science even if related to math. I used to be good at doing half lives, but I can't help you with this. Esp not with isotopes.

very sorry
• • • • •

Answer 57

its ok, do you know anyone who might be able to help?? and thank you soooooooooo much for your help!!

Answer 58

Not really, well you can look back into mathematics, and try to find someone of the top 99ers.
I keep seeing people like me that do all maths but don't play games with science-:(

Good luck !

Answer 59

Thanks :D