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CA Foundation · Quantitative Aptitude · Number Series, Coding-Decoding and Odd Man Out

Study this series: 3, 7, 15, 31, 63, 127, ?. What is the next number?

Each number in the series equals 2^n − 1, where n increases from 2 to 8. Alternatively, each term is double the previous plus one. Following this pattern, 127 × 2 + 1 = 255, which is the next number in the sequence.

  1. A255Correct
  2. B256
  3. C254
  4. D260

Explanation

The pattern is 2^n − 1 for n = 2, 3, 4, 5, 6, 7, 8. So: 2^2−1=3, 2^3−1=7, 2^4−1=15, 2^5−1=31, 2^6−1=63, 2^7−1=127, and 2^8−1=255. Alternatively, each term is obtained by doubling the previous term and adding 1: 3×2+1=7, 7×2+1=15, 15×2+1=31, 31×2+1=63, 63×2+1=127, 127×2+1=255. Option 256 is 2^8 but without the −1, and 254 and 260 do not follow the recursive pattern.

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