Question

Find the next term in the sequence: 3, 9, 19, 33, _

• A. \( 47 \)
• B. \( 49 \)
• C. \( 51 \)
• D. \( 53 \)

Hint:

A constant second-order difference indicates a quadratic sequence. Use this method to predict future terms efficiently.

Answer 1

The Correct Option is C

Finding the Pattern in the Sequence.
The given sequence: \[ 3, 9, 19, 33, \_ \] Finding first-order differences: \[ 9 - 3 = 6, \quad 19 - 9 = 10, \quad 33 - 19 = 14 \] Finding second-order differences: \[ 10 - 6 = 4, \quad 14 - 10 = 4 \] Since the second-order difference is constant (\(4\)), the sequence follows a quadratic pattern. The next first-order difference is: \[ 18 = 14 + 4 \] Thus, the next term in the sequence is: \[ 33 + 18 = 51 \]