5, 11, 23, 47, ?
Series Completion: 5, 11, 23, 47, ?
The task is to determine the next number in the sequence: 5, 11, 23, 47.
Identifying the Series Pattern
We need to find the rule connecting the numbers:
- First term: 5
- Second term: 11. Relationship: $(5 \times 2) + 1 = 10 + 1 = 11$.
- Third term: 23. Relationship: $(11 \times 2) + 1 = 22 + 1 = 23$.
- Fourth term: 47. Relationship: $(23 \times 2) + 1 = 46 + 1 = 47$.
The pattern is confirmed: each term is obtained by multiplying the previous term by 2 and adding 1. Mathematically, if $n_i$ is the i-th term, the next term $n_{i+1}$ is given by the formula: $n_{i+1} = (n_i \times 2) + 1$.
Calculating the Missing Term
Using the established pattern, we calculate the term following 47:
- Next Term = $(47 \times 2) + 1$
- Next Term = $94 + 1$
- Next Term = $95$
Therefore, the missing number in the series is 95.
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