Question

write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 +...+67
@ganeshie8 @dan815 @michele_Laino @nincompoop @solomonzelman @ paki @nnesha @undeadknight26

Answer 1

it is an arithmetic sequence, the first term is -8, whereas the last term is 67, furthermore, the constant of the sequence is:
-3-(-8)=2-(-3)=...?
please complete

Answer 2

5 @Michele_Laino

Answer 3

that's right!

Answer 4

now, we have to know how many terms are into your sequence. In order to do that, we have to use this general formula:
\[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]

Answer 5

where n is the number of terms, d=5, a_1=-8, and a_n=67

Answer 6

substituting those quantities, we can write:
\[67 = - 8 + \left( {n - 1} \right) \times 5\]

Answer 7

what is n?

Answer 8

16?

Answer 9

that's right! we have n= 16 terms in our sequence

Answer 10

so the requested sum S is given by the subsequent formula:
\[S = \frac{{{a_1} + {a_n}}}{2} \times n\]

Answer 11

where a_1=-8, a_n=67, n=16, please substitute into that formula above

Answer 12

\[S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{ - 8 + 67}}{2} \times 16 = ...?\]

Answer 13

472?

Answer 14

correct!

Answer 15

what do i do next?

Answer 16

we have completed your exercise

Answer 17

no i have to put it in sum notation @Michele_Laino

Answer 18

then I think that we have to write this:
\[\begin{gathered}
- 8 + \left( { - 3} \right) + 2 + 7 + 12 + 17 + + 22 + 27 + 32 + 37 + \hfill \\
+ 42 + 47 + 52 + 57 + 62 + 67 = 472 \hfill \\
\end{gathered} \]

Answer 19

is it right?

Answer 20

i need to write it in sum notation form?

Answer 21

sorry what do you mean with "notation form"?

Answer 22

summation notation

Answer 23

we can write this:
\[\Large \sum\limits_1^{16} { - 8 + \left( {n - 1} \right) \times 5} = 472\]

Answer 24

or:
\[\Large \sum\limits_1^{16} {\left[ { - 8 + \left( {n - 1} \right) \times 5} \right]} = 472\]

Answer 25

these are none of my options

Answer 26

which can be simplified as follows:
\[\Large \sum\limits_1^{16} {\left( {5n - 13} \right)} = 472\]

Answer 27

now?

Answer 28

nope

Answer 29

\[\Large \sum\limits_1^{16} n = 136\]
now?