Find the next term in the following series . `5I, 7J, 11L, 17O` , ?

Options

A. (a)`25` S
B. (b)`25` Y
C. (c)`20` P
D. (d)`18` C

Answer

To find the next term in the series `5I, 7J, 11L, 17O`, we can analyze the pattern in both the numbers and the letters.

### Step 1: Analyze the Numbers
The numbers in the series are: 5, 7, 11, 17.

- The difference between the first two numbers (5 and 7) is:
\( 7 - 5 = 2 \)

- The difference between the second and third numbers (7 and 11) is:
\( 11 - 7 = 4 \)

- The difference between the third and fourth numbers (11 and 17) is:
\( 17 - 11 = 6 \)

Now, let's summarize the differences:
- 2 (from 5 to 7)
- 4 (from 7 to 11)
- 6 (from 11 to 17)

We can see that the differences are increasing by 2 each time.

### Step 2: Predict the Next Number
Following the pattern of increasing differences, the next difference should be:
- \( 6 + 2 = 8 \)

Now, we add this difference to the last number in the series:
- \( 17 + 8 = 25 \)

### Step 3: Analyze the Letters
The letters in the series are: I, J, L, O.

- The sequence of letters corresponds to their positions in the alphabet:
- I is the 9th letter
- J is the 10th letter
- L is the 12th letter
- O is the 15th letter

Now, let's look at the differences in their positions:
- From I (9) to J (10): \( 10 - 9 = 1 \)
- From J (10) to L (12): \( 12 - 10 = 2 \)
- From L (12) to O (15): \( 15 - 12 = 3 \)

The differences in positions are:
- 1 (from I to J)
- 2 (from J to L)
- 3 (from L to O)

### Step 4: Predict the Next Letter
Following the pattern of increasing differences, the next difference should be:
- \( 3 + 1 = 4 \)

Now, we add this difference to the position of O (15):
- \( 15 + 4 = 19 \)

The 19th letter in the alphabet is S.

### Conclusion
Combining the results from both analyses, the next term in the series is:
**25S**