Question

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

-9 - 3 + 3 + 9 + ... + 81

Answer 1

What does it look like is happening to each term?

Answer 2

they are adding 6

Answer 3

Alright, and it starts from -9, how would you represent that using summation notation?

Answer 4

im not sure

Answer 5

\[\sum_{n=0}^{?} -9 + ?\] This is what you know so far. What could you add to the -9 to show that you're adding 6 , then 12, then 18, etc every time?

Answer 6

6n

Answer 7

That's right. Now how many times would you have to add 6n to get to 81?

Answer 8

15

Answer 9

Alright, \[\sum_{n=0}^{15} -9 + 6n\] This is how you build it in summation notation, or alternatively, \[\sum_{n=11}^{16} -9 + 6(n-1)\], same thing

Answer 10

The second one should read n=1, sorry

Answer 11

thank you so much for the help

Answer 12

You're welcome

Answer 13

write it like
\[\sum_{n=1}^{16}\left\{ -9+\left( n-1 \right)6 \right\}\]
\[=\sum_{n=1}^{16}\left( 6n-15 \right)\]

Answer 14

-9 - 3 + 3 + 9 + ... + 81
Write it following the order of PEMDAS.