The sequence is: 4, 7, 12, 19, 28, A, 52. Differences increase by successive odd numbers (+3, +5, +7, +9, +11, +13). Compute A^2 − 4^2.
Correct Answer: 1505
Introduction / Context:We are given an increasing sequence and an expression to evaluate after finding the missing term. The intended operation sign is exponentiation: A^2 minus 4^2.
Given Data / Assumptions:
- Sequence: 4, 7, 12, 19, 28, A, 52.
- Successive differences: +3, +5, +7, +9, +11, +13 (odd numbers in order).
- Interpret “A 2 – 4 = ?” as A^2 − 4^2 under standard formatting recovery.
Concept / Approach:Compute A using the difference pattern, then evaluate the requested expression with perfect squares.
Step-by-Step Solution:
4 → 7: +3; 7 → 12: +5; 12 → 19: +7; 19 → 28: +9.Next two differences should be +11 and +13.Therefore A = 28 + 11 = 39, and 39 + 13 = 52 (fits).Compute A^2 − 4^2 = 39^2 − 16 = 1521 − 16 = 1505.Verification / Alternative check:Using odd-number differences produces exact matches at each step, confirming A = 39.
Why Other Options Are Wrong:They result from misreading the exponent or using A*2 − 4; the recovered exponent form is consistent with the options.
Common Pitfalls:Missing the exponent indicator and interpreting as multiplication; always check difference patterns and option magnitudes.
Final Answer:1505.