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Find the next number in the series: 3, 7, 15, 31, 63, ?
127
125
129
131
127
The given number series follows a geometric pattern where each term is calculated by multiplying the previous term by two and adding one, or equivalently, as powers of two minus one. Following this pattern, the next number after sixty-three is sixty-three multiplied by two plus one, which equals one hundred twenty-seven. Thus, Option A is the correct choice.
The given number series follows a geometric pattern where each term is calculated by multiplying the previous term by two and adding one, or equivalently, as powers of two minus one. Following this pattern, the next number after sixty-three is sixty-three multiplied by two plus one, which equals one hundred twenty-seven. Thus, Option A is the correct choice.
The concept of binary systems and powers of two dates back to ancient Indian scholarship, notably found in Pingala's Chandahshastra in the context of poetic meters.
The difference between consecutive terms follows powers of two: four, eight, sixteen, thirty-two, and sixty-four.
Adding sixty-four to the last term sixty-three yields one hundred twenty-seven.
The general formula for this sequence is two to the power of n minus one.
Option B is one hundred twenty-five, which is incorrect as it does not fit the sequence pattern.
Option C is one hundred twenty-nine, which is incorrect and results from a calculation error.
Option D is one hundred thirty-one, which is incorrect and does not follow the doubling plus one rule.
A is correct тАФ one hundred twenty-seven is the next number in the series following the doubling and adding one pattern.
Number series questions frequently appear in reasoning sections of competitive exams like RRB and SSC, requiring quick recognition of arithmetic, geometric, and mixed difference patterns.
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