Find the next number in the pattern 1, 5, 14, 30, 55, ___?

hard 3 marks Class 4 · Mathematics · Play with Patterns

Answer

The correct answer is 91 — Step 4: Add this to the last term: $55 + 36 = 91$ .

Step-by-step solution

Step 1: Find differences between consecutive terms: $5 - 1 = 4,; 14 - 5 = 9,; 30 - 14 = 16,; 55 - 30 = 25$ .
Step 2: Notice the differences are $4, 9, 16, 25$ – consecutive perfect squares $2^{2}, 3^{2}, 4^{2}, 5^{2}$ .
Step 3: The next difference should be $6^{2} = 36$ .
Step 4: Add this to the last term: $55 + 36 = 91$ .

Common mistake: Adding the last difference again instead of the next square

Concept tested: Cumulative square pattern