Multiple choice

A sequence is given in which one term (or more terms) is missing. From the given options, choose the correct one that can complete the sequence. $1, 6, 15, ?, 45, 66, 91$

  1. $25$
  2. $26$
  3. $27$
  4. $28$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The pattern is n² + 1: 0²+1=1, 1²+1=2, 2²+1=5, 3²+1=10, 4²+1=17, 5²+1=26, 6²+1=37, 7²+1=50, 8²+1=65, 9²+1=82, 10²+1=101. Wait, this doesn't match. Let me recalculate: The actual pattern is odd numbers added to positions: 1+(2×0)=1, 1+(2×2.5)=6, 1+(2×7)=15, 1+(2×13.5)=28, 1+(2×22)=45. The correct pattern is (n²-1): for n=2:4-1=3 doesn't match. The working pattern is adding consecutive odd numbers starting from 1: 1+5=6, 6+9=15, 15+13=28, 28+17=45, 45+19=64 doesn't match 66. Actually: 1 (+5)=6 (+9)=15 (+13)=28 (+17)=45 (+21)=66 (+25)=91. The missing term is 28.