Select the number from among the given options that can replace the question mark (?) in the following series.
16, 35, ?, 217, 653, 1,309

The correct answer is 107.

To find the number that replaces the question mark (?), let us analyze the pattern of the given series:
16, 35, ?, 217, 653, 1,309

If we look at the transitions between successive terms, we can observe an alternating arithmetic pattern:

Step 1: Transition from the 1st term to the 2nd term (16 to 35):
We multiply the term by 2 and add 3:
$16\times 2+3=32+3=35$

Step 2: Transition from the 2nd term to the 3rd term (35 to ?):
Following the alternating pattern, we multiply the term by 3 and add 2:
$35\times 3+2=105+2=107$

Step 3: Let us verify this pattern with the subsequent terms to ensure it holds true.

Transition from the 3rd term to the 4th term (107 to 217):
We multiply by 2 and add 3:
$107\times 2+3=214+3=217$

Transition from the 4th term to the 5th term (217 to 653):
We multiply by 3 and add 2:
$217\times 3+2=651+2=653$

Transition from the 5th term to the 6th term (653 to 1,309):
We multiply by 2 and add 3:
$653\times 2+3=1306+3=1309$

Since the pattern matches perfectly throughout the entire series, the missing number is 107.