Final answer:
The recursive sequences provided as options do not consistently produce the sequence 2, -10, 26. After testing each one against the sequence, it was found that none of the options A, B, C, or D correctly generate the given sequence. The changes between the terms -12 and +36 suggest a different pattern not listed among the options.
Step-by-step explanation:
The student is asking for the recursive sequence that can generate the sequence 2, -10, 26. To find out which recursive formula applies, we should look at how each term relates to the previous one. From 2 to -10, the difference is -12 because -10 = 2 + (-12). From -10 to 26, the difference is +36 because 26 = -10 + 36. Since no consistent difference is immediately visible, we will test each given option:
- Option A (an = an-1 - 12): This would mean every term is 12 less than the previous. For our case, it would give 2, -10 (correct), but the next term would be -22, not 26.
- Option B (an = an-1 + 8): This would mean every term is 8 more than the previous one. For our sequence, it would produce 2, 10 (incorrect).
- Option C (an = an-1 + 16): This would produce 2, 18 (incorrect).
- Option D (an = an-1 - 16): This option leads to 2, -14 (incorrect).
None of the options provided would produce the sequence 2, -10, 26 consistently. Each step needs to be checked against the sequence for correctness.
However, notice that the changes between the terms are multiples of 4 (-12 and +36 are divisible by 4), so a pattern using these specific differences is not provided in the options.