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

1. Michele_Laino

the first term is: ${a_1} = 2 \times 1 + 4 = ...?$

2. anonymous

I would just plug that in?

3. Michele_Laino

the first term is given by replacing n with 1 into your formula

4. Michele_Laino

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

5. Michele_Laino

what is a_1?

6. anonymous

8?

7. Michele_Laino

hint: $\large {a_1} = 2 \times 1 + 4 = 2 + 4 = ...?$

8. anonymous

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

10. Michele_Laino

the first term is a1=6 right?

11. Michele_Laino

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

now we have this: $\Large n\left( {n + 1} \right) + 4n = {n^2} + n + 4n = {n^2} + 5n$

13. anonymous

n(2n+4) ?

14. Michele_Laino

I think that it is: n(n+1)+4n

15. anonymous

no it's n(n+1)+4n ??

16. Michele_Laino

that's right!

17. anonymous

yay!! thank you!!

18. Michele_Laino

:)

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