15 + 3 = 18

As per my opinion

on odd place

on every alternate place observe the numbers and you will get to know that numbers are like 15 _ 16 _17_18__
now come to even place
17_19_20_21

we can see here
there should be 18 instead of 17
hence option (a) would be the answer

Explanation:

The given number series is: 15 17 16 19 17 20 18 21

To find the wrong number, we need to identify the pattern followed in the series and then check which number does not fit the pattern.

Pattern Analysis:

Upon observing the given series, we can notice the following pattern:

- The first number is 15 and the next number is obtained by adding 2 to the previous number (15 + 2 = 17).
- The third number is obtained by subtracting 1 from the second number (17 - 1 = 16).
- The fourth number is obtained by adding 3 to the third number (16 + 3 = 19).
- The fifth number is obtained by subtracting 2 from the fourth number (19 - 2 = 17).
- The sixth number is obtained by adding 3 to the fifth number (17 + 3 = 20).
- The seventh number is obtained by subtracting 2 from the sixth number (20 - 2 = 18).
- The eighth number is obtained by adding 3 to the seventh number (18 + 3 = 21).

Identifying the Wrong Number:

Now, let's compare the given series with the pattern:

- The first number 15 is correct as it follows the pattern.
- The second number 17 is correct as it follows the pattern.
- The third number 16 is correct as it follows the pattern.
- The fourth number 19 is correct as it follows the pattern.
- The fifth number 17 is incorrect as it does not follow the pattern. According to the pattern, it should be obtained by subtracting 2 from the fourth number (19 - 2 = 17), but in the given series, it is repeated.
- The sixth number 20 is correct as it follows the pattern.
- The seventh number 18 is correct as it follows the pattern.
- The eighth number 21 is correct as it follows the pattern.

Therefore, the wrong number in the given series is 17.

Conclusion:

The correct answer is option 'A' (17).