Letter Sequence Pattern Analysis

The question presents a sequence where letters are assigned numerical values. We need to find the pattern to determine the value for the letter M.

• Given: H = 17, I = 19, J = 21
• Alphabetical Positions: H is the 8th letter, I is the 9th, J is the 10th, and M is the 13th.

Identifying the Numerical Pattern

Let's analyze the relationship between the letter's position in the alphabet and its assigned value.

• H (8th letter): Value = 17
• I (9th letter): Value = 19
• J (10th letter): Value = 21

Observe the difference between consecutive values:

• $19 - 17 = 2$
• $21 - 19 = 2$

The values increase by 2 for each subsequent letter in the sequence shown. Let's test a formula relating the alphabetical position ($n$) to the value ($V$). A possible formula is $V = 2n + c$.

• For H (n=8): $17 = 2 \times 8 + c \implies 17 = 16 + c \implies c = 1$.
• Test for I (n=9): $V = 2 \times 9 + 1 = 18 + 1 = 19$. (Matches)
• Test for J (n=10): $V = 2 \times 10 + 1 = 20 + 1 = 21$. (Matches)

The pattern holds: Value $= 2 \times (\text{Alphabetical Position}) + 1$.

Calculating the Value for M

M is the 13th letter of the alphabet ($n=13$). Using the established pattern:

• Value for M $= 2 \times 13 + 1$
• Value for M $= 26 + 1$
• Value for M $= 27$

Therefore, M = 27.