Multiple choice

Choose the correct alternative from the given ones that will complete the series. $1 , 2 , 6 , 15 , 31 , \dots$

  1. $55$
  2. $58$
  3. $56$
  4. $59$
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C Correct answer
Explanation

The series follows the pattern of adding consecutive increasing numbers: 1, 1+1=2, 2+4=6, 6+9=15, 15+16=31. The added numbers are squares: 1, 1+1²=2, 2+2²=6, 6+3²=15, 15+4²=31. Continuing this pattern: 31+5²=31+25=56. Alternatively, differences are: 1, 4, 9, 16 (squares of 1, 2, 3, 4). Next difference should be 25, giving 31+25=56.

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