Directions: Insert the missing number: 4, - 8, 16, - 32, 64, (.....)

### Concept & Logic The sequence is a geometric progression where each term is multiplied by a constant negative factor. ### Step-by-Step Solution Let's observe the ratio between consecutive terms: - $-8 / 4 = -2$ - $16 / -8 = -2$ - $-32 / 16 = -2$ - $64 / -32 = -2$ The common ratio is $-2$. To find the next term, multiply the last term by $-2$: $64 \times -2 = -128$ ### Exam Strategy & Shortcut When a series alternates between positive and negative numbers, it strongly indicates multiplication by a negative number. Check the ratios immediately rather than differences. ### Common Pitfall Ignoring the alternating signs and assuming an addition/subtraction pattern, or calculating $64 \times 2 = 128$ and missing the negative sign. ### Final Answer Therefore, the correct answer is **- 128**.