Analysis:
To find the missing term in the given sequence (1, 6, 15, ?, 45, 66, 91), we need to identify the pattern or rule followed by the numbers in the sequence.

Pattern:
Upon observing the sequence, we can see that the pattern is not linear or arithmetic. Therefore, we need to consider other possibilities such as quadratic or exponential patterns.

Quadratic Pattern:
Let's first check if the given sequence follows a quadratic pattern. We can do this by finding the differences between consecutive terms.

1, 6, 15, ?, 45, 66, 91

The differences are:

(6-1) = 5, (15-6) = 9, (?, 15) = x, (45-?), (66-45) = 21, (91-66) = 25

The differences between the differences are:

(9-5) = 4, (x-9) = y, (21-y), (25-21) = 4

If the sequence followed a quadratic pattern, the second order of differences would be constant. However, in this case, the second order of differences is not constant, indicating that the sequence does not follow a quadratic pattern.

Exponential Pattern:
Now, let's check if the given sequence follows an exponential pattern. We can do this by finding the ratios between consecutive terms.

1, 6, 15, ?, 45, 66, 91

The ratios are:

6/1 = 6, 15/6 ≈ 2.5, ?/15 = x, 45/? = y, 66/45 ≈ 1.47, 91/66 ≈ 1.38

If the sequence followed an exponential pattern, the ratios between consecutive terms would be constant. However, in this case, the ratios are not constant, indicating that the sequence does not follow an exponential pattern either.

Conclusion:
After analyzing the given sequence, it does not follow any clear pattern or rule. Therefore, it is not possible to determine the missing term with certainty based on the given information.