Question

A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. \[ 5, 11, 24, 51, 106, \_ ? \]

• A. 122
• B. 217
• C. 120
• D. 153

Hint:

Look for patterns in the differences between terms, and use second differences to find the next term in sequences with quadratic growth.

Answer 1

The Correct Option is B

Step 1: To find the pattern in the series, calculate the difference between successive terms: \[ 11 - 5 = 6, \quad 24 - 11 = 13, \quad 51 - 24 = 27, \quad 106 - 51 = 55. \] Step 2: The second differences are: \[ 13 - 6 = 7, \quad 27 - 13 = 14, \quad 55 - 27 = 28. \] Step 3: The second differences are doubling, so the next second difference should be \( 28 \times 2 = 56 \).
Step 4: The next first difference is: \[ 55 + 56 = 111. \] Step 5: The next term in the sequence is: \[ 106 + 111 = 217. \] Thus, the missing term is \( \boxed{217} \).