To determine the most likely next step in the series [tex]\(10 A, 21 b, 32 C, 43 d, 54 E, 65 f\)[/tex], let's analyze both the numerical and alphabetical components separately.
### Numerical Pattern
Let's observe the given sequence of numbers: [tex]\( 10, 21, 32, 43, 54, 65 \)[/tex].
Calculate the differences between consecutive numbers:
- [tex]\(21 - 10 = 11\)[/tex]
- [tex]\(32 - 21 = 11\)[/tex]
- [tex]\(43 - 32 = 11\)[/tex]
- [tex]\(54 - 43 = 11\)[/tex]
- [tex]\(65 - 54 = 11\)[/tex]
We notice that the difference is consistently 11. Therefore, to find the next number in the series:
[tex]\[ 65 + 11 = 76 \][/tex]
### Alphabetical Pattern
Now, let's analyze the sequence of letters: [tex]\( A, b, C, d, E, f \)[/tex].
Observing the pattern:
- The uppercase 'A' is followed by the lowercase 'b'.
- The uppercase 'C' is followed by the lowercase 'd'.
- The uppercase 'E' is followed by the lowercase 'f'.
This indicates an alternating pattern between uppercase and lowercase letters.
Based on this pattern, the next letter should be:
- Uppercase, following the lowercase 'f'.
Thus, the next letter would be 'G'.
### Conclusion
Combining both the numerical and alphabetical patterns, the next term in the series should be:
[tex]\[ 76 G \][/tex]
So, the most likely next step in the series is:
A. 76 G
