Finding the Next Term in the Series

This question asks us to identify the pattern in the given series and determine the next term. The series is: 1D3, 3H5, 5L7, ______, ______

Let's break down each term into its components: the first number, the letter, and the second number.

Analyzing the Number Pattern

Let's look at the first number in each term:

• Term 1: 1
• Term 2: 3
• Term 3: 5

We can see that the first numbers form a sequence where each term is obtained by adding 2 to the previous term ($1+2=3$, $3+2=5$). Following this pattern, the next first number should be $5+2=7$. The subsequent number would be $7+2=9$.

Now, let's look at the second number in each term:

• Term 1: 3
• Term 2: 5
• Term 3: 7

Similarly, the second numbers also form a sequence where each term is obtained by adding 2 to the previous term ($3+2=5$, $5+2=7$). Following this pattern, the next second number should be $7+2=9$. The subsequent number would be $9+2=11$.

Analyzing the Letter Pattern

Now let's look at the letter in each term:

• Term 1: D
• Term 2: H
• Term 3: L

To find the pattern, let's consider the position of these letters in the English alphabet (A=1, B=2, C=3, and so on).

• D is the 4th letter.
• H is the 8th letter.
• L is the 12th letter.

The positions form a sequence: 4, 8, 12. This is an arithmetic progression where each term is obtained by adding 4 to the previous term ($4+4=8$, $8+4=12$). Following this pattern, the next letter's position should be $12+4=16$. The 16th letter of the alphabet is P.

The subsequent letter's position would be $16+4=20$. The 20th letter is T.

Combining the Patterns

Let's combine the next elements we found for each part:

• Next first number: 7
• Next letter: P (16th letter)
• Next second number: 9

Putting these together, the next term in the series is 7P9.

Let's find the term after that as well:

• Next first number (after 7): 9
• Next letter (after P): T (20th letter)
• Next second number (after 9): 11

So the series would continue: 1D3, 3H5, 5L7, 7P9, 9T11, ...

Comparing with Options

The next term we found is 7P9. Let's check the given options:

1. 7 P 9
2. 7 R 9
3. 7 N 9
4. 7 L 9

Our calculated next term, 7P9, matches Option 1.

Step-by-Step Solution Summary

1. Analyze the first numbers: 1, 3, 5. Pattern: add 2. Next number is 7.
2. Analyze the second numbers: 3, 5, 7. Pattern: add 2. Next number is 9.
3. Analyze the letters: D, H, L. Positions are 4, 8, 12. Pattern: add 4 to position. Next position is 16, which corresponds to letter P.
4. Combine the next elements: First number (7), Letter (P), Second number (9) gives 7P9.

Revision Table: Series Pattern Summary

Additional Information: Types of Series Reasoning

Series reasoning questions are common in logic and aptitude tests. They can involve different types of patterns:

• Number Series: Arithmetic progression (constant difference), geometric progression (constant ratio), squares, cubes, prime numbers, Fibonacci sequence, alternating patterns, etc.
• Letter Series: Based on alphabetical positions, skipping letters, reverse alphabetical order, patterns in vowel/consonant usage, etc.
• Alpha-Numeric Series: Combination of number and letter patterns, often requiring analysis of each component separately, as seen in this question.
• Mixed Series: Patterns involving symbols, figures, or other elements along with numbers or letters.

Solving these questions requires careful observation, breaking down the elements, and identifying the underlying rules that govern the progression from one term to the next.