Understanding the Series Pattern

The question asks us to find the missing terms in the series: I-10, L-13, O-16, ?, ?, X-25. This is a combined series where each term consists of a letter and a number connected by a hyphen. To solve this, we need to analyze the pattern in the letter sequence and the number sequence separately.

Analyzing the Letter Sequence

Let's look at the letters in the given terms:

• First term letter: I
• Second term letter: L
• Third term letter: O
• Sixth term letter: X

We need to find the letters for the fourth and fifth terms.

Let's find the position of these letters in the English alphabet:

• I is the 9th letter.
• L is the 12th letter.
• O is the 15th letter.
• X is the 24th letter.

Now, let's find the difference in alphabetical position between consecutive letters:

• Position of L - Position of I = \(12 - 9 = 3\)
• Position of O - Position of L = \(15 - 12 = 3\)

The pattern for the letter sequence appears to be adding 3 to the alphabetical position of the previous letter to get the next letter. Let's apply this pattern to find the missing letters.

• Fourth term letter: The letter after O (15th) should be at position \(15 + 3 = 18\). The 18th letter is R.
• Fifth term letter: The letter after R (18th) should be at position \(18 + 3 = 21\). The 21st letter is U.
• Sixth term letter (Check): The letter after U (21st) should be at position \(21 + 3 = 24\). The 24th letter is X, which matches the last term given in the series.

So, the missing letters are R and U.

Analyzing the Number Sequence

Now let's look at the numbers in the given terms:

• First term number: 10
• Second term number: 13
• Third term number: 16
• Sixth term number: 25

We need to find the numbers for the fourth and fifth terms.

Let's find the difference between consecutive numbers:

• Second number - First number = \(13 - 10 = 3\)
• Third number - Second number = \(16 - 13 = 3\)

The pattern for the number sequence appears to be adding 3 to the previous number to get the next number. Let's apply this pattern to find the missing numbers.

• Fourth term number: The number after 16 should be \(16 + 3 = 19\).
• Fifth term number: The number after 19 should be \(19 + 3 = 22\).
• Sixth term number (Check): The number after 22 should be \(22 + 3 = 25\), which matches the last term given in the series.

So, the missing numbers are 19 and 22.

Combining the Patterns to Find Missing Terms

To find the missing terms, we combine the corresponding missing letters and numbers:

• Fourth missing term: The fourth letter is R and the fourth number is 19. So the term is R-19.
• Fifth missing term: The fifth letter is U and the fifth number is 22. So the term is U-22.

The complete series with the missing terms filled in is: I-10, L-13, O-16, R-19, U-22, X-25.

Verifying the Solution with Options

Let's compare the missing terms we found (R-19, U-22) with the given options:

The first option, R-19, U-22, matches our calculated missing terms.

Conclusion

By analyzing the separate patterns in the letter sequence (adding 3 to the alphabetical position) and the number sequence (adding 3), we determined the missing terms are R-19 and U-22.

Revision Table: Key Concepts for Series Problems

Additional Information on Solving Series Questions

Solving series completion questions often requires careful observation and testing different types of patterns. Here are some common approaches:

• Arithmetic Progression: Numbers increase or decrease by a constant difference (like the number series in this problem).
• Geometric Progression: Numbers are multiplied or divided by a constant factor.
• Alphabetical Progression: Letters move forward or backward in the alphabet by a fixed number of steps or follow patterns based on position.
• Mixed Patterns: Sometimes patterns alternate (e.g., add 2, then subtract 1, then add 2, etc.).
• Positional Patterns: The position of a number or letter relates to its value or the pattern itself.
• Combined Patterns: As seen in this problem, different parts of a term (like letter and number) can follow independent patterns.

Always check if the identified pattern holds true for all the given terms in the series before concluding.