Alright class, let's analyze the given series step by step:
The series is: [tex]$10 A, 21 b, 32 C, 43 d, 54 E, 65 f$[/tex]
1. Identify the pattern in the numbers:
- Going through the numbers, we observe the following:
- 10 to 21: difference of [tex]\(21 - 10 = 11\)[/tex]
- 21 to 32: difference of [tex]\(32 - 21 = 11\)[/tex]
- 32 to 43: difference of [tex]\(43 - 32 = 11\)[/tex]
- 43 to 54: difference of [tex]\(54 - 43 = 11\)[/tex]
- 54 to 65: difference of [tex]\(65 - 54 = 11\)[/tex]
So, each number in the sequence is increasing by 11.
To find the next number:
[tex]\[ 65 + 11 = 76 \][/tex]
2. Identify the pattern in the letters:
- Looking at the letters and their cases:
- A (uppercase)
- b (lowercase)
- C (uppercase)
- d (lowercase)
- E (uppercase)
- f (lowercase)
The letters alternate between uppercase and lowercase in each step, and they follow the alphabetical order.
To find the next letter:
- The letter after 'f' is 'g'.
- Considering the pattern, since 'f' is lowercase, 'g' must be uppercase:
- Next letter is 'G'
Combining these two, the most likely next step in the series is:
[tex]\[ 76 \, G \][/tex]
3. Match with the given options:
- A. 7 fg
- B. 66 g
- C. 765
- D. 76 g
- E. 76 G
Hence, the correct answer is E. 76 G.
