Question

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

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

Answer 1

Do you see how the pattern is working? If so, can you tell me the next term after '6' ?

Answer 2

yes it's adding 5, so the next term would be 11

Answer 3

very good

Answer 4

so it turns out this is an arithmetic sequence because we keep adding 5 each time. The '5' is the common difference

so d = 5

the first term is a = -9

Answer 5

you plug those two pieces of info into the formula below

t = a + d(n-1)

t = -9 + 5(n-1)

t = ???? ... what do you get when you simplify?

Answer 6

-9 + 5n

Answer 7

not quite

Answer 8

you forgot about distributing fully

Answer 9

5(n-1) = 5*n + 5*(-1) = 5n - 5

use that to simplify

Answer 10

-9 + 5n - 5?

Answer 11

keep going

Answer 12

-14 + 5n? i'm lost lol

Answer 13

yep or 5n - 14

Answer 14

now set 5n - 14 equal to 66

5n - 14 = 66

solve for n to get the n = ???

Answer 15

16

Answer 16

correct

Answer 17

n = 16 means that 66 is the 16th term of that sequence given

Answer 18

-9 is the first term, so when n = 1

Answer 19

are you familiar with sigma notation?

Answer 20

yes i'm just not sure how these numbers work into it

Answer 21

-9 -4 + 1 + 6 + ... 66
so each term goes up by +5 so the slope is 5.
5n
the first term (where everything starts from is 9), so
-9+5n

Now, whichTH term is 66?
66=-9+5(n-1)
75=5(n-1)
15=(n-1)
n=16

So, there are 16 terms starting from n=1.
Now all that remains is the sigma notation

Answer 22

Start with a sigma symbol (basically a funky looking E)

Answer 23

at the bottom we will have k = 1. We use k instead of n because it's more common (at least in my experience)



the bottom is where we start. The top is where we end up. So think of it as climbing a mountain.

Answer 24

so we write 16 at the top to signify "stop adding when you get to the 16th term"