Final answer:
After calculating the first differences of the sequence (24, 10, 26, 32), it's clear there is no consistent first difference, so the options provided do not reflect a correct pattern for the given sequence.
Step-by-step explanation:
The pattern for the 1st difference for the sequence 9, 33, 43, 69, 101 can be found by calculating the difference between consecutive terms in the sequence.
- Difference between 33 and 9 is 24.
- Difference between 43 and 33 is 10.
- Difference between 69 and 43 is 26.
- Difference between 101 and 69 is 32.
Unfortunately, based on the differences we calculated, there is no consistent pattern in the first differences. Thus, none of the provided options (a) +12, (b) +14, (c) +18, or (d) +22 is the correct pattern for the first difference of the given sequence. Perhaps there was an error in the given sequence or options, as the differences do not match the pattern of a linear sequence which would have a constant first difference.