Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which of the following is most likely the next step in the series?

[tex]\[10 A, 21 b, 32 C, 43 d, 54 E, 65 f\][/tex]

A. 76 G
B. 765
C. 66 g
D. 7 fg
E. 76 g
F. 66 G

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