Question

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

Answer 1

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

Answer 2

you can use the formula for sums of geometric and arithmetic series.

Answer 3

Sum of arithmetic finite series:
\[S=(a_1+a_k)*k/2\]

Answer 4

what does k mean in the formula

Answer 5

k means the number of last term, which is in your sequence is 66.
u have an arithmetic series that starts with term -9 and has difference 5.
Here is your sequence:
\[a_n=-9+5(n-1)\]

Answer 6

so k will mean here, the number of term which is equal to 66.
To find k do the following:
\[66=-9+5(k-1)\]
\[66+9=5(k-1)\]
\[75/5=k-1\]
\[15+1=k=16\]

Answer 7

so the last term is 6th and you can substitute this number into formula
\[ S=(-9+66)*6/2=57*3=171\]

Answer 8

the answer is 171, @allydiaz

Answer 9

All the options are in summation notation @ksanka

Answer 10

How would I write it in summation notation form?

Answer 11

nth term

a1 + d(n-1)
-9 + 5(n-1)
-9 + 5n - 5
5n - 14

so the general nth term is 5n - 14

we'll use k instead of n since that's common for summations. So we'll have 5k - 14 instead

The summation will look like this

\[\LARGE \sum_{k=1}^{16}(5k-14)\]

the funky looking E, written like this \(\Large \Sigma\) is the capital Greek letter sigma. Sigma for Sum

the "k = 1" portion tells us where to start (start at the first term)

the 16 up top tells us where to stop: we stop when we get to the 16th term

the (5k-14) off to the right tells us what we're actually adding up. The k's will vary from 1 to 16