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anonymous
 one year ago
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
anonymous
 one year ago
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

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0it 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, 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
 one year ago
Best ResponseYou've already chosen the best response.0where n is the number of terms, d=5, a_1=8, and a_n=67

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0substituting those quantities, we can write: \[67 =  8 + \left( {n  1} \right) \times 5\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0that's right! we have n= 16 terms in our sequence

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so the requested sum S is given by the subsequent formula: \[S = \frac{{{a_1} + {a_n}}}{2} \times n\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0where a_1=8, a_n=67, n=16, please substitute into that formula above

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{  8 + 67}}{2} \times 16 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have completed your exercise

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no i have to put it in sum notation @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0then I think that we have to write this: \[\begin{gathered}  8 + \left( {  3} \right) + 2 + 7 + 12 + 17 + + 22 + 27 + 32 + 37 + \hfill \\ + 42 + 47 + 52 + 57 + 62 + 67 = 472 \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i need to write it in sum notation form?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0sorry what do you mean with "notation form"?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we can write this: \[\Large \sum\limits_1^{16} {  8 + \left( {n  1} \right) \times 5} = 472\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0or: \[\Large \sum\limits_1^{16} {\left[ {  8 + \left( {n  1} \right) \times 5} \right]} = 472\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0these are none of my options

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0which can be simplified as follows: \[\Large \sum\limits_1^{16} {\left( {5n  13} \right)} = 472\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[\Large \sum\limits_1^{16} n = 136\] now?
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