Directions: Find the wrong number in the series. 5, 15, 30, 135, 405, 1215, 3645

### Concept & Logic The series appears to be a geometric progression where each term is multiplied by a constant factor, or perhaps an alternating multiplier. Let's find the ratios. ### Step-by-Step Solution 1. Calculate the ratio between consecutive terms: - $15 / 5 = 3$ - $30 / 15 = 2$ (This breaks the pattern) - $135 / 30 = 4.5$ - $405 / 135 = 3$ - $1215 / 405 = 3$ - $3645 / 1215 = 3$ 2. The clear pattern towards the end is multiplying by $3$. Let's apply this from the beginning. - $5 \times 3 = 15$ - $15 \times 3 = 45$ (Instead of 30) - $45 \times 3 = 135$ (Matches the sequence!) 3. The pattern holds if we replace $30$ with $45$. Thus, $30$ is the wrong term. ### Exam Strategy & Shortcut When a series grows very fast, it's almost certainly based on multiplication. Look at the later terms where the pattern is usually cleaner to avoid small-number anomalies. $405 \times 3 = 1215$, establishing the $\times 3$ rule. ### Common Pitfall Assuming a complex alternating pattern like $\times 3, \times 2, \times 4.5$ instead of realizing one wrong number disrupts a simple $\times 3$ pattern. ### Final Answer Therefore, the correct answer is **30**.