Question

Find the missing number: 2, 6, 20, 42, 110, ____

• A. 126
• B. 156
• C. 176
• D. 196

Hint:

Write each number as a product of two consecutive integers, then notice the smaller integer in each pair is always one less than a prime number.

Answer 1

The Correct Option is B

Step 1: Split each term into a product of two consecutive whole numbers.
2 = 1 x 2, 6 = 2 x 3, 20 = 4 x 5, 42 = 6 x 7, 110 = 10 x 11. Each term is n times (n+1) for some n.

Step 2: Look at just the smaller number in each pair.
These smaller numbers are 1, 2, 4, 6, 10. Each one is exactly 1 less than a prime number: 1 = 2-1, 2 = 3-1, 4 = 5-1, 6 = 7-1, 10 = 11-1. So the primes used, in order, are 2, 3, 5, 7, 11.

Step 3: Find the next prime in that list.
After 2, 3, 5, 7, 11 comes 13. So the next smaller number in the pair is 13-1 = 12, and the pair becomes 12 x 13.

Step 4: Multiply out the next term.
12 x 13 = 156.

Final Answer:
The missing number is 156. \[ \boxed{156} \]