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anonymous

  • one year ago

Please help me. I will medal & fan!!!!!!!!** :) If the nth term of a sequence is 2n + 4, what is the sum of the first n terms? A.) n(n+1)+4n B.) n(n+1)/2 +n C.) n(2n+4) D.) n(n+1)(2n+1) /6 + 2n(n+1) E.) 2n(n+1)/n

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  1. Michele_Laino
    • one year ago
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    the first term is: \[{a_1} = 2 \times 1 + 4 = ...?\]

  2. anonymous
    • one year ago
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    I would just plug that in?

  3. Michele_Laino
    • one year ago
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    the first term is given by replacing n with 1 into your formula

  4. Michele_Laino
    • one year ago
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    the requested sum S is given by the subsequent formula: \[S = \frac{{{a_1} + {a_n}}}{2} \times n\]

  5. Michele_Laino
    • one year ago
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    what is a_1?

  6. anonymous
    • one year ago
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    8?

  7. Michele_Laino
    • one year ago
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    hint: \[\large {a_1} = 2 \times 1 + 4 = 2 + 4 = ...?\]

  8. anonymous
    • one year ago
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    I'm just a numskull and don't understand any of this. I thank you for time and effort. I will just guess at this point... Thank you, though. :)

  9. Michele_Laino
    • one year ago
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    please wait

  10. Michele_Laino
    • one year ago
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    the first term is a1=6 right?

  11. Michele_Laino
    • one year ago
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    now we have to substitute so we can write: \[\large \begin{gathered} S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{6 + 2n + 4}}{2} \times n = \frac{{10 + 2n}}{2} \times n = \hfill \\ \hfill \\ = \left( {5 + n} \right)n = 5n + {n^2} \hfill \\ \end{gathered} \]

  12. Michele_Laino
    • one year ago
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    now we have this: \[\Large n\left( {n + 1} \right) + 4n = {n^2} + n + 4n = {n^2} + 5n\]

  13. anonymous
    • one year ago
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    n(2n+4) ?

  14. Michele_Laino
    • one year ago
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    I think that it is: n(n+1)+4n

  15. anonymous
    • one year ago
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    no it's n(n+1)+4n ??

  16. Michele_Laino
    • one year ago
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    that's right!

  17. anonymous
    • one year ago
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    yay!! thank you!!

  18. Michele_Laino
    • one year ago
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    :)

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