katieb
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Michele_Laino
  • Michele_Laino
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
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
that's right!

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Michele_Laino
  • Michele_Laino
now, we have to know how many terms are into your sequence. In order to do that, we have to use this general formula: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\]
Michele_Laino
  • Michele_Laino
where n is the number of terms, d=5, a_1=-8, and a_n=67
Michele_Laino
  • Michele_Laino
substituting those quantities, we can write: \[67 = - 8 + \left( {n - 1} \right) \times 5\]
Michele_Laino
  • Michele_Laino
what is n?
anonymous
  • anonymous
16?
Michele_Laino
  • Michele_Laino
that's right! we have n= 16 terms in our sequence
Michele_Laino
  • Michele_Laino
so the requested sum S is given by the subsequent formula: \[S = \frac{{{a_1} + {a_n}}}{2} \times n\]
Michele_Laino
  • Michele_Laino
where a_1=-8, a_n=67, n=16, please substitute into that formula above
Michele_Laino
  • Michele_Laino
\[S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{ - 8 + 67}}{2} \times 16 = ...?\]
anonymous
  • anonymous
472?
Michele_Laino
  • Michele_Laino
correct!
anonymous
  • anonymous
what do i do next?
Michele_Laino
  • Michele_Laino
we have completed your exercise
anonymous
  • anonymous
no i have to put it in sum notation @Michele_Laino
Michele_Laino
  • Michele_Laino
then I think that we have to write this: \[\begin{gathered} - 8 + \left( { - 3} \right) + 2 + 7 + 12 + 17 + + 22 + 27 + 32 + 37 + \hfill \\ + 42 + 47 + 52 + 57 + 62 + 67 = 472 \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
is it right?
anonymous
  • anonymous
i need to write it in sum notation form?
Michele_Laino
  • Michele_Laino
sorry what do you mean with "notation form"?
anonymous
  • anonymous
summation notation
Michele_Laino
  • Michele_Laino
we can write this: \[\Large \sum\limits_1^{16} { - 8 + \left( {n - 1} \right) \times 5} = 472\]
Michele_Laino
  • Michele_Laino
or: \[\Large \sum\limits_1^{16} {\left[ { - 8 + \left( {n - 1} \right) \times 5} \right]} = 472\]
anonymous
  • anonymous
these are none of my options
Michele_Laino
  • Michele_Laino
which can be simplified as follows: \[\Large \sum\limits_1^{16} {\left( {5n - 13} \right)} = 472\]
Michele_Laino
  • Michele_Laino
now?
anonymous
  • anonymous
nope
Michele_Laino
  • Michele_Laino
\[\Large \sum\limits_1^{16} n = 136\] now?

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