Find the missing term in the s...

Find the missing term in the sequence 5, 11, 17, ?, 31, 41.
A. 19
B. 21
C. 23
D. 25

Answer

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Hint: In the sequence, all the terms are prime numbers. Thus consider all prime numbers upto 50 and find the missing number among it.

Complete step by step answer:

We have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.

If we look closer, we can see that they are all prime numbers.

We know that a prime number is a number which is exactly divisible by 1 and itself.

Now let us look into the given sequence: 5, 11, 17, ?, 31, 41.

Let us write the prime numbers upto 50.

2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37, 41, 43, 47.

By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,

5, 11, 17, 23, 31, 41.

Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.

Option C is the correct answer.

Note: If we consider the given sequence as an arithmetic progression then the series will be 5, 11, 17, 23, 29, 35…. By comparing the first three terms, we can say that it has a common difference of 6 between each term. We may get the answer 23, but the method can’t be right.