Multiple choice

Find the missing term in the following number series: $1, 32, 101, 232, 455, ?$

  1. $806$
  2. $732$
  3. $708$
  4. $832$
  5. $706$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pattern is n³+n+1 for consecutive integers starting from n=0: 0³+0+1=1, 3³+3+1=31≠32 (adjustment: 3³+4+1=32), 4³+4+1=69≠101. Better pattern: consecutive cubes plus the number: 1³+0=1, 3³+5=32, 4³+37=101. Actual pattern: each term is n³+(n-2) for n starting at 1: 1³+(-1)=0≠1. Simpler: 1, 32=2⁵, 101, 232, 455. Working backwards: differences 31, 69, 131, 223. Second differences: 38, 62, 92 (increasing by 24, 30). Next second difference: 92+36=128, so next first difference: 223+128=351, so next term: 455+351=806, matching option A.