Question

Find the missing term of the series: 61, 74, 89, 97, ..., 121, 145

• A. 117
• B. 118
• C. 116
• D. None of these

Hint:

In series problems, always check the differences step by step. If differences are irregular, look for alternating patterns or jumps that fit consistently with later terms.

Answer 1

The Correct Option is A

Step 1: Observe the series
Given terms: \(61, 74, 89, 97, ____, 121, 145\). Step 2: Check differences between consecutive terms
\[ 74 - 61 = 13,\quad 89 - 74 = 15,\quad 97 - 89 = 8 \] Now between the missing term and \(97\), and then to \(121\): \[ 121 - (____) = ?, \quad 145 - 121 = 24 \] Step 3: Look for a pattern
The differences are not uniform but show an alternating or mixed pattern: \[ 13,\; 15,\; 8,\; 20,\; 24 \] So, after \(97\), the difference should be \(20\). Step 4: Find the missing term
\[ 97 + 20 = 117 \] Thus, the missing term is \(117\). \(\boxed{117}\)