Directions: Find out the wrong number in each sequence 1, 2, 6, 15, 31, 56, 91

### Concept & Logic The sequence is formed by adding squares of consecutive natural numbers. ### Step-by-Step Solution Let's look at the differences between consecutive terms: - $2 - 1 = 1 = 1^2$ - $6 - 2 = 4 = 2^2$ - $15 - 6 = 9 = 3^2$ - $31 - 15 = 16 = 4^2$ - $56 - 31 = 25 = 5^2$ - Let the next term be $x$. - $x - 56$ should be equal to $6^2 = 36$. - So, $x = 56 + 36 = 92$. The given term is 91, which is incorrect. It should be 92. ### Exam Strategy & Shortcut When a series increases at an accelerating rate but not as fast as a geometric progression, checking the differences is a solid strategy. Here, the differences form a very familiar pattern of perfect squares. ### Common Pitfall Simple calculation errors in finding the differences or recognizing the squares. ### Final Answer Therefore, the correct answer is **91**.