Understanding the Alphabet-Number Series Pattern

This question asks us to identify the pattern in a given series of terms, where each term consists of a letter followed by a number, and then find the missing term that continues the pattern. The series is Z49, D90, H131, L172, P213, ?

To solve this type of series, we need to examine the pattern for the alphabetical part and the numerical part separately.

Analyzing the Alphabetical Pattern

Let's look at the letters in the series:

• Z
• D
• H
• L
• P
• ?

We can find the positional value of each letter in the English alphabet (A=1, B=2, ..., Z=26).

• Z is the 26th letter.
• D is the 4th letter.
• H is the 8th letter.
• L is the 12th letter.
• P is the 16th letter.

Let's see the difference in positional values between consecutive letters. Since the alphabet wraps around (after Z comes A), we can think of the steps taken from one letter to the next.

• From Z to D: Z → A → B → C → D. This is a jump of 4 letters forward (26 → 1 → 2 → 3 → 4, which is effectively $+4$ positions considering the wrap-around: $26+4 = 30 \equiv 4 \pmod{26}$ if we map A-Z to 1-26, or $26+4 = 30 \equiv 4 \pmod{26}$ using 1-26 map, $0+4 = 4$ if Z is considered 0 and A is 1). Let's simply count the steps: Z(26) + 4 letters = D(4).
• From D to H: D is 4th, H is 8th. $8 - 4 = 4$. This is a jump of 4 letters.
• From H to L: H is 8th, L is 12th. $12 - 8 = 4$. This is a jump of 4 letters.
• From L to P: L is 12th, P is 16th. $16 - 12 = 4$. This is a jump of 4 letters.

The pattern for the letters is consistently moving forward by 4 positions in the alphabet, wrapping around from Z to A.

So, to find the next letter, we add 4 to the positional value of P (16th letter): $16 + 4 = 20$.

The 20th letter of the alphabet is T.

Analyzing the Numerical Pattern

Now let's look at the numbers in the series:

• 49
• 90
• 131
• 172
• 213
• ?

Let's find the difference between consecutive numbers:

• Difference between 90 and 49: $90 - 49 = 41$.
• Difference between 131 and 90: $131 - 90 = 41$.
• Difference between 172 and 131: $172 - 131 = 41$.
• Difference between 213 and 172: $213 - 172 = 41$.

The pattern for the numbers is consistently adding 41 to the previous number.

So, to find the next number, we add 41 to the last number in the series (213): $213 + 41 = 254$.

Combining the Patterns

The next term in the series will be the next letter followed by the next number.

The next letter is T.

The next number is 254.

Therefore, the missing term is T254.

Checking the Options

Let's compare our result with the given options:

The term T254 matches the pattern we found for both the letters and the numbers.