What is the missing number in the table? x | 1 2 3 4 5 y | 6 36 216 ??? 7,776 A. 252 B. 396 C. 864 D. 1,296

Answer: 1,296

Explanation: Subject: Math — pattern recognition / sequences (geometric progression) and exponential functions. The y-values form a geometric sequence with common ratio 6 (36/6 = 6, 216/36 = 6, 7,776/1,296 = 6). That yields the rule y = 6^x, so for x = 4, y = 6^4 = 1,296.

Steps:

1. Compute successive ratios: 36 ÷ 6 = 6, 216 ÷ 36 = 6, 7,776 ÷ 216 = 36 (but check via inferred middle term). The consistent small-step ratio is 6, suggesting y multiplies by 6 each time x increases by 1.
2. Deduce formula y = 6^x (since 6^1 = 6, 6^2 = 36, 6^3 = 216, 6^5 = 7,776).
3. Evaluate at x = 4: 6^4 = 6 × 6 × 6 × 6 = 1,296.
4. Verify: 6^5 = 6 × 1,296 = 7,776 matches the given value for x = 5.