Question

Please Help!!

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

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

Answer 1

Do you need help at first with figuring out what number term is 81 in the sequence ?

Answer 2

yeah

Answer 3

d= ?

Answer 4

i know that the first term is -9 and the difference is 6

Answer 5

Okay good for the start

Answer 6

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

\(\large\color{darkviolet}{ a_n=-9+6(80-1) }\) good with this one ?

Answer 7

a_n=-9+6(81-1)

Answer 8

My bad it is like this, \(\large\color{darkviolet}{ 81=-9+6(n-1) }\)

Answer 9

\(\large\color{darkviolet}{ 81=-9+6(n-1) }\)

\(\large\color{darkviolet}{ 90=6(n-1) }\)

\(\large\color{darkviolet}{ 15=(n-1) }\)

\(\large\color{darkviolet}{ n=14 }\)

Answer 10

What have I found just now ?

Answer 11

that 81 is the 14th term

Answer 12

Yes, so there are 14 terms and 81 is the 14th.

Answer 13

Can you take an attempt on the sigma ?

Answer 14

one sec

Answer 15

sure:)

Answer 16

\[\sum_{n=0}^{15}\left( -9+6n \right)\]

Answer 17

yes, but then put 13 on the top, so that you have 14 numbers
0,1,2,3 .... 12,13.
not 15 terms, and certainly not 16 as you wrote.

Answer 18

i wrote 15 because it starts off with 14 terms but my only answer could either be 15 on top or infinity

Answer 19

\(\large\color{darkviolet}{ 15=(n-1) }\) here is the error
\(\large\color{darkviolet}{ 16=n }\) b/c you add 1 to both sides.

Answer 20

\[\sum_{n=0}^{15}~(-9+6n)~~~\rm ~~~~ is~~~correct:)\]

Answer 21

yay :D, can you help me with a few more?

Answer 22

Yes, I can try :P

Answer 23

thanks