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Identify the next number in the sequence: 3, 7, 13, 21, 31, ?
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Solution: Step 1: Analyze the differences between consecutive terms: 7 - 3 = 4, 13 - 7 = 6, 21 - 13 = 8, 31 - 21 = 10.
Step 2: Identify the pattern in differences: 4, 6, 8, 10, ... (increasing by 2 each time).
Step 3: Predict the next difference: 10 + 2 = 12.
Step 4: Calculate the next term: 31 + 12 = 43.