Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81

summation of the quantity negative nine plus six n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to infinity
summation of the quantity negative nine plus six n from n equals zero to infinity

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KerryEye KerryEye · Answer 1 · 2020-02-13T16:38:18+01:00

Answer:

Option A: [tex]$ \sum_{n = 1}^{15} {\textbf{- 9 + 6 n}} $[/tex]

Step-by-step explanation:

We are given with the series - 9 - 3 + 3 + 9 + . . . . + 81.

Note that the second term is obtained by adding 6 to the first term.

Each consecutive term is obtained by adding 6 to its previous term.

Therefore, we should be adding six two times to get the third term from the first term.

Putting it Mathematically, we get: - 9 + 6n

This gives all the terms of the sequence. Since, we have to add all the terms we take the summation.

Also, note that 81 is the 15 th term.

Therefore, - 9 - 3 + 3 + 9 + . . . . + 81 = [tex]$ \sum_{n = 1}^{15} {- 9 + 6 n} $[/tex]

Hence, the answer.