15, 38, 57, 74, 87, ?

Options

A. 84
B. 86
C. 96
D. 98

Explanation

To find the next number in the series: 15, 38, 57, 74, 87, we can follow these steps:

### Step 1: Identify the pattern in the series
We start by looking at the differences between consecutive numbers in the series.

- From 15 to 38:
\( 38 - 15 = 23 \)

- From 38 to 57:
\( 57 - 38 = 19 \)

- From 57 to 74:
\( 74 - 57 = 17 \)

- From 74 to 87:
\( 87 - 74 = 13 \)

### Step 2: List the differences
Now, we have the following differences:
- 23
- 19
- 17
- 13

### Step 3: Analyze the differences
Next, we observe the differences:
- The first difference is 23.
- The second difference is 19 (which is 4 less than 23).
- The third difference is 17 (which is 2 less than 19).
- The fourth difference is 13 (which is 4 less than 17).

### Step 4: Predict the next difference
We can see that the differences are not consistent, but they seem to be decreasing. The pattern of differences appears to be related to prime numbers:
- 23 (prime)
- 19 (prime)
- 17 (prime)
- 13 (prime)

The next prime number in this sequence would be 11.

### Step 5: Calculate the next number
Now, we add this next difference (11) to the last number in the series (87):
\[ 87 + 11 = 98 \]

### Conclusion
Thus, the next number in the series is **98**.

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