Understanding the Alphanumeric Series Pattern

This question asks us to find the next term in the given alphanumeric series: \(10M-30, 15O-27, 20K-24, 25Q-21, ?\) To solve this, we need to identify the distinct patterns governing the numbers and the letter.

Analyzing the Series Components

The series can be broken down into three parts for each term: the first number, the letter, and the second number. We will analyze each part separately.

First Number Pattern Analysis

Let's look at the sequence of the first numbers:

• Term 1: 10
• Term 2: 15
• Term 3: 20
• Term 4: 25

We observe the difference between consecutive terms:

• \(15 - 10 = 5\)
• \(20 - 15 = 5\)
• \(25 - 20 = 5\)

The pattern is that the first number increases by 5 in each subsequent term. Therefore, the next first number will be \(25 + 5 = 30\).

Letter Pattern Analysis

Now let's examine the sequence of letters:

• Term 1: M
• Term 2: O
• Term 3: K
• Term 4: Q

To understand the pattern, we find the position of each letter in the English alphabet:

• M is the 13th letter.
• O is the 15th letter.
• K is the 11th letter.
• Q is the 17th letter.

The sequence of positions is: 13, 15, 11, 17.

Let's consider the positions at odd intervals (1st, 3rd) and even intervals (2nd, 4th) separately:

• Odd intervals (1st term, 3rd term): M (13), K (11). The pattern is \(13 - 2 = 11\).
• Even intervals (2nd term, 4th term): O (15), Q (17). The pattern is \(15 + 2 = 17\).

The next term we are looking for is the 5th term, which corresponds to an odd interval sequence. Following the pattern established by M and K, we subtract 2 from the position of K:

• Position for the 5th term letter = \(11 - 2 = 9\).

The 9th letter of the alphabet is I.

Second Number Pattern Analysis

Finally, let's analyze the sequence of the second numbers:

• Term 1: 30
• Term 2: 27
• Term 3: 24
• Term 4: 21

We observe the difference between consecutive terms:

• \(27 - 30 = -3\)
• \(24 - 27 = -3\)
• \(21 - 24 = -3\)

The pattern is that the second number decreases by 3 in each subsequent term. Therefore, the next second number will be \(21 - 3 = 18\).

Constructing the Missing Term

By combining the results from our analysis:

• The next first number is 30.
• The next letter is I.
• The next second number is 18.

Thus, the missing term in the series is 30I-18.