anonymous
  • anonymous
What is the sum of the first 19 terms of an arithmetic series with a rate of increase of 7 and a7 = 46? 1,197 1,273 1,373 1,423 1,327
Mathematics
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SOLVED
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katieb
  • katieb
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Michele_Laino
  • Michele_Laino
since the general formula for the n-th term is: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\] where d is constant of your sequance, namely d=7, then we can write: \[\Large \begin{gathered} {a_7} = {a_1} + \left( {7 - 1} \right) \times 7 \hfill \\ \hfill \\ 46 = {a_1} + \left( {7 - 1} \right) \times 7 \hfill \\ \end{gathered} \] please solve for a_1
Michele_Laino
  • Michele_Laino
hint: \[\Large 46 = {a_1} + 42\]

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Michele_Laino
  • Michele_Laino
after that we have to compute a_19, using the same general formula above: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\] so we have: \[\Large {a_{19}} = {a_1} + \left( {19 - 1} \right) \times 7 = ...?\]
Michele_Laino
  • Michele_Laino
then the requested sum S is given by the subsequent formula: \[\Large S = \frac{{{a_1} + {a_{19}}}}{2} \times 19 = ...?\]
anonymous
  • anonymous
I got it!! Thank you!
Michele_Laino
  • Michele_Laino
thanks! :)

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