Final answer:
The sum -9 - 4 + 1 + 6 + ... + 66 written in summation notation is Σ from i=1 to 16 of (-9 + 5(i-1)). This notation captures the pattern of the series, where each term increases by 5 from the previous term, starting at -9.
Step-by-step explanation:
To write the sum -9 - 4 + 1 + 6 + ... + 66 using summation notation, we first need to identify the pattern of the series. We can see that the difference between consecutive terms is increasing by 5 each time (-9 to -4 is +5, -4 to 1 is +5, 1 to 6 is +5, and so on). The starting term is -9, and we're adding 5(n-1) to get each subsequent term, where n is the position of the term in the sequence. The nth term of the sequence can be represented as an = -9 + 5(n-1).
Since the last term given is 66, we need to find out what n gives us 66 in the formula for an. By setting an equal to 66, we get 66 = -9 + 5(n-1), which simplifies to 75 = 5(n-1), and further on to n = 16. This tells us the series has 16 terms.
Putting this into summation notation, we get Σi=116 (-9 + 5(i-1)), which is the summation from i equals 1 to 16 of (-9 + 5 times (i minus 1)).