Final answer:
After applying the formulas for the arithmetic sequence to find the number of terms and the sum of the sequence, the calculated sum is 150, which does not match any of the answer choices provided. Hence, there seems to be an error in the question or answer choices.
Step-by-step explanation:
The question asks to find the sum of the arithmetic sequence −3 + 1 + 5 + 9 + … + 33. To find this sum, we need to identify the number of terms, the first term, and the last term.
The first term of the sequence is −3, and the common difference is the difference between any two consecutive terms, which is 4 in this case (1 - (−3) = 4).
We can find the last term to be 33 by simply observing the sequence given in the question. Now, to calculate the number of terms (n) in the sequence, use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the last term, a1 is the first term, n is the number of terms, and d is the common difference. After finding the number of terms, use the sum formula for an arithmetic sequence, which is Sn = ½n(a1 + an), where Sn is the sum of the first n terms.
To find n, we rearrange and solve the formula for the nth term:
n = ((an - a1) / d) + 1
n = ((33 - (−3)) / 4) + 1
n = (36 / 4) + 1
n = 9 + 1
n = 10
Now we apply the formula for the sum of an arithmetic sequence:
S10 = ½(10)(−3 + 33)
S10 = ½(10)(30)
S10 = 5(30)
S10 = 150
However, the answer calculated seems to be larger than all of the answer choices, indicating that there may have been an error in the calculation process. Checking the calculation, the error was in the sum formula application. The correct sum is:
S10 = ½(10)(-3 + 33)
S10 = 5(30)
S10 = 150
The correct answer is therefore not listed in the answer choices provided, and we must notify the student of the discrepancy.