## 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

1. 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

2. anonymous

5 @Michele_Laino

3. Michele_Laino

that's right!

4. 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: $\Large {a_n} = {a_1} + \left( {n - 1} \right)d$

5. Michele_Laino

where n is the number of terms, d=5, a_1=-8, and a_n=67

6. Michele_Laino

substituting those quantities, we can write: $67 = - 8 + \left( {n - 1} \right) \times 5$

7. Michele_Laino

what is n?

8. anonymous

16?

9. Michele_Laino

that's right! we have n= 16 terms in our sequence

10. Michele_Laino

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

11. Michele_Laino

where a_1=-8, a_n=67, n=16, please substitute into that formula above

12. Michele_Laino

$S = \frac{{{a_1} + {a_n}}}{2} \times n = \frac{{ - 8 + 67}}{2} \times 16 = ...?$

13. anonymous

472?

14. Michele_Laino

correct!

15. anonymous

what do i do next?

16. Michele_Laino

17. anonymous

no i have to put it in sum notation @Michele_Laino

18. Michele_Laino

then I think that we have to write this: $\begin{gathered} - 8 + \left( { - 3} \right) + 2 + 7 + 12 + 17 + + 22 + 27 + 32 + 37 + \hfill \\ + 42 + 47 + 52 + 57 + 62 + 67 = 472 \hfill \\ \end{gathered}$

19. Michele_Laino

is it right?

20. anonymous

i need to write it in sum notation form?

21. Michele_Laino

sorry what do you mean with "notation form"?

22. anonymous

summation notation

23. Michele_Laino

we can write this: $\Large \sum\limits_1^{16} { - 8 + \left( {n - 1} \right) \times 5} = 472$

24. Michele_Laino

or: $\Large \sum\limits_1^{16} {\left[ { - 8 + \left( {n - 1} \right) \times 5} \right]} = 472$

25. anonymous

these are none of my options

26. Michele_Laino

which can be simplified as follows: $\Large \sum\limits_1^{16} {\left( {5n - 13} \right)} = 472$

27. Michele_Laino

now?

28. anonymous

nope

29. Michele_Laino

$\Large \sum\limits_1^{16} n = 136$ now?