Question

What is the missing number in the following series: 61, 57, 53, ___, 45

a. 50
b. 49
c. 48
d. 51

(Explanation would be appreciated)

Answer 1

Given 61, 57, 53, ... , I ask myself what the first term is. That's 61. How do I get 57 from 61? By subracting 4. From 57, how do I get 53? By subtracting 4. Thus, this is an arithmetic sequence with common difference -4.

Looking at 61, 57, 53, ___, 45 again, I ask myself what would happen if I were to subtract 4 from 53. I'd get 49. As a check, I'd subtract 4 from 49. Do I get 45? Yes.

So the missing number here is 49.