Question

What is the next number in this series ?

4, 6, 12, 18, 30, 42, 60, ?
A) 71
B) 72
C) 73
D) 69

Answer 1

it would be 72 answer I am sure please market as brainliest

Answer 2

Answer:

Step-by-step explanation:

Given:

A series $4, 6, 12, 18, 30, 42, 60, ?$

Find:

Next number in the given series

Solution:

• Find out the pattern of occurence of numbers in the series.

Close inspection will reveal that each number in the list is sandwiched between two prime numbers.

    $4$ → occurs between prime numbers $3$ and $5$

    $6$ → occurs between prime numbers $5$ and $7$

    $12$ →  occurs between prime numbers $11$ and $13$

    $18$ →  occurs between prime numbers $17$ and $19$

    $30$ →  occurs between prime numbers $29$ and $31$

    $42$ →   occurs between prime numbers $41$ and $43$

    $60$ →  occurs between prime numbers $59$ and $61$

From above pattern ,it is observed that the next number must be the middle element of next two prime numbers. After $61$ , the next prime numbers will be $67, 71,73 ,79 ........$As the next number in series falls between prime numbers, it must lie between $71$ and $73$ which is $72$.

Hence, $72$ comes next to $60$ in the given series.

Now the series becomes $4, 6, 12, 18, 30, 42, 60, 72$

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