Question

6,12,30,60,102,156,?​

Answer 1

Answer:

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Answer 2

The complete sequence of numbers will be 6,12,30,60,102,156,222​  .

The given numbers form a sequence which is neither an arithmetic, geometric or harmonic sequence.

To find the missing number let us find the difference between the given numbers in the series.

$12-6=6\\30-12=18\\60-30=30\\102-60=42\\156-102=54$

Thus the number which are the differences of the given numbers are

$6 , 18 , 30 , 42$  and $54.$

These numbers form an AP(arithmetic progression) with a common difference of 12.

Therefore the next number of the sequence will be $54+12=66$ as the numbers are in an arithmetic sequence.

So the difference between the next number of the original sequence and 156 is 66 .

The required number = $156+66=222$ .

Therefore the next number of the original sequence is 222 .

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