Which of the following numbers will replace the question marks (?) in the given series?
1, 6, 15, 28, ?, ?, 91

The correct option is 45, 66.

Step-by-step explanation:

To determine the numbers that replace the question marks in the series: 1, 6, 15, 28, ?, ?, 91, let us first analyze the differences between consecutive terms:

$6-1=5$

$15-6=9$

$28-15=13$

Now, observe the sequence of differences (5, 9, 13). The second difference between consecutive terms is constant:

$9-5=4$

$13-9=4$

Since the difference increases by 4 at each step, we can find the subsequent differences and missing terms:

Next difference: $13+4=17$

First missing term (?): $28+17=45$

Following difference: $17+4=21$

Second missing term (?): $45+21=66$

To verify our result, we can check the next term in the series:

Next difference: $21+4=25$

Last term: $66+25=91$

The pattern matches the last term (91) perfectly. Therefore, the numbers that replace the question marks are 45 and 66.