Select the number from among the given options that can replace the question mark (?) in the following series. 6, 5, 18, 10, 54, 20, ?, 40
The given series is 6, 5, 18, 10, 54, 20, ?, 40.
Let's analyze the series to identify the pattern. We can observe two distinct subsequences within the series:
- Subsequence 1 (First, third, fifth, etc.): 6, 18, 54, ... This is a geometric progression where each term is multiplied by 3 to get the next term (6 * 3 = 18, 18 * 3 = 54).
- Subsequence 2 (Second, fourth, sixth, etc.): 5, 10, 20, 40, ... This is a geometric progression where each term is multiplied by 2 to get the next term (5 * 2 = 10, 10 * 2 = 20, 20 * 2 = 40).
Following this pattern, the missing term (?) belongs to Subsequence 1. Therefore, we continue the pattern: 54 * 3 = 162.
Thus, the number that replaces the question mark is 162.
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