Fill in the missing numbers and state the rules for these sequences: a) 3, 5, 9, 15, 23, 33, , 37, , 61

Here are the missing numbers and rules for the sequences:

a) 3, 5, 9, 15, 23, 33, ___, 37, ___, 61

Step 1: Analyze the initial part of the sequence: 3, 5, 9, 15, 23, 33.
Calculate the differences between consecutive terms:
$5 - 3 = 2$
$9 - 5 = 4$
$15 - 9 = 6$
$23 - 15 = 8$
$33 - 23 = 10$
The differences are increasing by 2 each time (2, 4,