To solve this problem, we need to analyze the patterns in both the letters and the numbers separately.
Step 1: Analyzing the letters:
1. The series given is B, D, G, K, ?
2. Convert the letters into their corresponding positions in the alphabet:
- B -> 2nd position
- D -> 4th position
- G -> 7th position
- K -> 11th position
3. Find the differences between the positions of the letters:
- From B (2) to D (4): [tex]\( 4 - 2 = 2 \)[/tex]
- From D (4) to G (7): [tex]\( 7 - 4 = 3 \)[/tex]
- From G (7) to K (11): [tex]\( 11 - 7 = 4 \)[/tex]
4. The differences between each step are increasing by 1 each time. Therefore, the next difference should be [tex]\( 4 + 1 = 5 \)[/tex].
5. To find the next letter, add this difference to the last position:
- From K (11) to the next letter: [tex]\( 11 + 5 = 16 \)[/tex]
- The 16th letter in the alphabet is P.
So, the next letter in the series is P.
Step 2: Analyzing the numbers:
1. The series of numbers given is 25, 23, 19, 13, ?
2. Calculate the differences between adjacent numbers:
- From 25 to 23: [tex]\( 25 - 23 = 2 \)[/tex]
- From 23 to 19: [tex]\( 23 - 19 = 4 \)[/tex]
- From 19 to 13: [tex]\( 19 - 13 = 6 \)[/tex]
3. The differences between each step in the numbers are increasing by 2 each time. Therefore, the next difference should be [tex]\( 6 + 2 = 8 \)[/tex].
4. To find the next number, subtract this difference from the last number:
- From 13 to the next number: [tex]\( 13 - 8 = 5 \)[/tex]
So, the next number in the series is 5.
Step 3: Conclusion
Combining the results from the analysis of both the letters and the numbers:
The next item in the series is P, 5. Therefore, the correct answer is:
B) P
