Question Details

Find out the missing term of the number series given below.

15, 34, 57, 86, ?, 154

Options

A

123

B

121

C

117

D

115

E

113

Show Answer

Correct Answer :

Option C

117

Solution :

To find the missing term of the number series, let's analyze the differences between consecutive terms in the series: 15, 34, 57, 86, ?, 154.

Let's calculate the difference between each consecutive term:
First difference: 34-15=19
Second difference: 57-34=23
Third difference: 86-57=29

Notice the sequence of the differences: 19, 23, 29, ...
These numbers are consecutive prime numbers starting from 19.

Following this pattern, the next prime number after 29 is 31.
Therefore, the next difference in the series should be 31.

Let's add 31 to the last known term (86) to find the missing term:
Missing term = 86+31=117

To verify the pattern, let's check if the next step works with the prime number following 31, which is 37:
Next term = 117+37=154

This matches the final term in the series (154). Thus, the pattern is consistent and correct.

The correct answer is 117.

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