Question

Given the sequence: \( 5, 6, 15, \_, 89, 170, 291 \), find the missing number.

• A. 30
• B. 35
• C. 40
• D. 45

Hint:

When finding missing numbers in sequences, check the differences between terms and the second differences to identify the pattern.

Answer 1

The Correct Option is C

Step 1: Identifying the pattern in the sequence.

The differences between consecutive terms are: \[ 6 - 5 = 1, \quad 15 - 6 = 9, \quad 89 - 15 = 74, \quad 170 - 89 = 81, \quad 291 - 170 = 121. \]

There seems to be a growing pattern in the differences.

The second differences are: \[ 9 - 1 = 8, \quad 74 - 9 = 65, \quad 81 - 74 = 7, \quad 121 - 81 = 40. \]

This indicates that the missing number is \( 40 \).

Thus, the correct answer is \( 40 \).