What is the missing number in the pattern given below?
1, 6, 15, ____, 45, 66, 91

The correct answer is 28 (Option 28).

To find the missing number in the sequence, let us analyze the differences between consecutive terms.

Given sequence:
1, 6, 15, ____, 45, 66, 91

Let us write down the differences between consecutive known terms:

$6-1=5$

$15-6=9$

Now check the differences between the known terms at the end of the sequence:

$66-45=21$

$91-66=25$

Notice the pattern in the differences between consecutive terms:
5, 9, ____, ____, 21, 25

The difference between consecutive differences is constant (+4):

$9-5=4$

$25-21=4$

Following this pattern, the step differences increment by 4 each time:
First difference = 5
Second difference = 5 + 4 = 9
Third difference = 9 + 4 = 13
Fourth difference = 13 + 4 = 17
Fifth difference = 17 + 4 = 21
Sixth difference = 21 + 4 = 25

Now we add the third difference (13) to the 3rd term (15) to find the missing term:

$15+13=28$

We can verify this result by adding the fourth difference (17) to 28:

$28+17=45$

Since this matches the 5th term in the sequence, the missing number is indeed 28.