Question

Find the next number in series: 2, 5, 10, 17, 26, 37, 50, 65, ?,101

• A. 92
• B. 82
• C. 81
• D. 86

Hint:

When the differences increase by consecutive odd numbers, try expressing the series in terms of squares.

Answer 1

The Correct Option is B

Concept: The terms follow the pattern \(n^2+1\).

Step 1: Verify the pattern. \[ 1^2+1=2 \] \[ 2^2+1=5 \] \[ 3^2+1=10 \] \[ 4^2+1=17 \] \[ 5^2+1=26 \] \[ 6^2+1=37 \] \[ 7^2+1=50 \] \[ 8^2+1=65 \]

Step 2: Find the next term. \[ 9^2+1=81+1=82 \] Therefore, the next number is \[ \boxed{82} \]