To find the next term in the series 4A, 7B, 12D, 19G, we will analyze both the numerical and alphabetical patterns step by step.
### Step 1: Analyze the numerical pattern
We will look at the numbers in the series: 4, 7, 12, 19.
- The difference between 4 and 7 is:
\[
7 - 4 = 3
\]
- The difference between 7 and 12 is:
\[
12 - 7 = 5
\]
- The difference between 12 and 19 is:
\[
19 - 12 = 7
\]
Now, we can see that the differences are increasing by 2 each time:
- 3, 5, 7
### Step 2: Determine the next difference
Following the pattern, the next difference should be:
\[
7 + 2 = 9
\]
### Step 3: Calculate the next number
Now, we add this difference to the last number in the series:
\[
19 + 9 = 28
\]
### Step 4: Analyze the alphabetical pattern
Next, we will look at the letters in the series: A, B, D, G.
- The position of A is 1.
- The position of B is 2.
- The position of D is 4.
- The position of G is 7.
Now, let's find the differences in the positions:
- The difference between A (1) and B (2) is:
\[
2 - 1 = 1
\]
- The difference between B (2) and D (4) is:
\[
4 - 2 = 2
\]
- The difference between D (4) and G (7) is:
\[
7 - 4 = 3
\]
We can see that the differences are increasing by 1 each time:
- 1, 2, 3
### Step 5: Determine the next letter
Following the pattern, the next difference should be:
\[
3 + 1 = 4
\]
Now, we add this difference to the position of G (7):
\[
7 + 4 = 11
\]
### Step 6: Find the corresponding letter
The 11th letter of the alphabet is K.
### Final Result
Thus, the next term in the series is:
\[
28K
\]
### Summary
The next term in the series is **28K**.
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