Question Details:

The given sequence is 7, 7, 13, 37, 97, ?.

Options:

A) 237
B) 247
C) 217
D) 227
E) 257

Correct Answer:

The correct answer is option C) 217.

Explanation:

The given sequence is not following any specific pattern.

Let's see the difference between consecutive terms of the given sequence:

- The difference between the first and second terms is 0.
- The difference between the second and third terms is 6.
- The difference between the third and fourth terms is 24.
- The difference between the fourth and fifth terms is 60.

Now, let's see the difference between the consecutive differences:

- The difference between the first and second differences is 6.
- The difference between the second and third differences is 18.
- The difference between the third and fourth differences is 36.

Therefore, we can conclude that the next term will be:

97 + (60 + 36) = 193 + 60 = 253

But this is not given in the options.

Alternatively, we can try to find a pattern in the given sequence by looking at the prime numbers.

- 7 is a prime number.
- 13 is a prime number.
- 37 is a prime number.
- 97 is a prime number.

Therefore, the next term should also be a prime number.

The only option that is a prime number is option C) 217.

Hence, the correct answer is option C) 217.