Finding the Missing Term in the Sequence: 6A4, 12D7, 20G11, 30J16, ?

This question asks us to identify the pattern in the given sequence and find the missing term. The sequence consists of terms that have three parts: a starting number, a letter, and an ending number. Let's break down the pattern for each part.

Analyzing the Starting Number Pattern

Consider the first number in each term:

• Term 1: $6$
• Term 2: $12$
• Term 3: $20$
• Term 4: $30$

Let's look at the difference between consecutive numbers:

• $12 - 6 = 6$
• $20 - 12 = 8$
• $30 - 20 = 10$

The difference is increasing by $2$ each time ($6, 8, 10$). The next difference should therefore be $10 + 2 = 12$. So, the next starting number is $30 + 12 = 42$.

Analyzing the Letter Pattern

Now, let's examine the letter in each term:

• Term 1: $A$
• Term 2: $D$
• Term 3: $G$
• Term 4: $J$

Let's find the difference in positions in the alphabet:

• $A$ is the $1^{st}$ letter.
• $D$ is the $4^{th}$ letter. Difference: $4 - 1 = 3$.
• $G$ is the $7^{th}$ letter. Difference: $7 - 4 = 3$.
• $J$ is the $10^{th}$ letter. Difference: $10 - 7 = 3$.

The pattern is that each subsequent letter is 3 positions after the previous one in the alphabet. The next letter should be 3 positions after $J$ (the $10^{th}$ letter). This means the $10 + 3 = 13^{th}$ letter.

The $13^{th}$ letter of the alphabet is $M$.

Analyzing the Ending Number Pattern

Finally, let's look at the last number in each term:

• Term 1: $4$
• Term 2: $7$
• Term 3: $11$
• Term 4: $16$

Let's find the difference between consecutive numbers:

• $7 - 4 = 3$
• $11 - 7 = 4$
• $16 - 11 = 5$

The difference is increasing by $1$ each time ($3, 4, 5$). The next difference should therefore be $5 + 1 = 6$. So, the next ending number is $16 + 6 = 22$.

Combining the Patterns to Find the Missing Term

We found the patterns for each component:

• Starting Number: The next number is $42$.
• Letter: The next letter is $M$.
• Ending Number: The next number is $22$.

Combining these, the missing term in the sequence is 42M22.