1, 1, 3, 5, 11, 21, 43, ?
Number Series Reasoning: Finding the Missing Term
The question asks us to identify the missing number in the given number series: 1, 1, 3, 5, 11, 21, 43, ?
Given Number Series
The series is: 1, 1, 3, 5, 11, 21, 43, ?
Series Pattern Analysis
Let's analyze the relationship between consecutive terms to find the underlying pattern. We observe the following pattern:
- Term 1 to Term 2: No clear arithmetic operation, remains 1.
- Term 2 to Term 3: $1 \times 2 + 1 = 3$
- Term 3 to Term 4: $3 \times 2 - 1 = 5$
- Term 4 to Term 5: $5 \times 2 + 1 = 11$
- Term 5 to Term 6: $11 \times 2 - 1 = 21$
- Term 6 to Term 7: $21 \times 2 + 1 = 43$
The pattern involves multiplying the previous term by 2 and then alternating between adding 1 and subtracting 1.
The operation applied depends on the position or the previous operation. Starting from the second term:
- The operation sequence is: +1, -1, +1, -1, +1, ...
Calculating the Missing Term
To find the term replacing the question mark (the 8th term), we apply the next operation in the sequence to the 7th term (43).
Since the last operation was '+1' (to get 43 from 21), the next operation must be '-1'.
- Missing Term = (Previous Term $\times$ 2) - 1
- Missing Term = $(43 \times 2) - 1$
- Missing Term = $86 - 1$
- Missing Term = $85$
Therefore, the number that replaces the question mark is 85.
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Select the number from among the given options that can replace the question mark (?) in the following series.
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Select the number that can replace the question mark (?) in the following series.
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