Final answer:
The series -13, -7, -1, 5, 11 is an arithmetic sequence with a common difference of 6. The correct sigma notation representation of this sequence is Σ from k=0 to 4 of (-13+6k), which corresponds to option (d).
Step-by-step explanation:
The question asks which of the following represents the series -13 + (-7) + (-1) + 5 + 11. To determine this, we need to note the pattern in the series and find the expression that could generate this sequence.
The series starts at -13 and then each term increases by 6: -13, -7, -1, 5, 11. This follows an arithmetic sequence with a common difference of 6. Therefore, the general term for an arithmetic series of this nature is given by the first term plus the common difference times the position in the series subtracted by one (since the first term is for the zeroth position).
Therefore, substituting the first term (-13) and the common difference (6), the nth term of the sequence is represented by -13 + 6(n-1). Therefore, if we express this in sigma notation, starting at k=0 and going to 4 (since there are 5 terms), the representation will be:
Σ⁴
k=0
(-13+6k)
Which corresponds to option (d) among the provided choices.