Multiple choice

Find the missing number in the following number series: $1 \quad 2 \quad ? \quad 36 \quad 85 \quad 166$

  1. 17

  2. 13

  3. 11

  4. 8

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The pattern is n³ - n² for n=1,2,3,4,5: 1³-1²=0, 2³-2²=4, 3³-3²=18, 4³-4²=48, 5³-5²=100. The given series 1,2,11,36,85,166 follows n³ - n² + n - 1: for n=1:1-1+1-1=0 (but we have 1), for n=3:27-9+3-1=20 (we have 11). The actual pattern is: for odd positions use 1³-0=1, 3³+3=30, 5³+5=130 (doesn't match). Alternative: terms are n² + 2n - 2 starting from n=1 for odd terms: 1²+2(1)-2=1, 3²+2(3)-2=11, 5²+2(5)-2=33 (we have 36). Testing shows the pattern is actually n² + 2n - 2: 1²+2(1)-2=1, 2²+2(2)-2=6 (not 2), 3²+2(3)-2=11 ✓. The pattern isn't perfectly consistent. However, 11 fits the gap between 2 and 36.