3, - 6, 12, 4, 20,?

what is the next number in the sequence?

The next term in the sequence 3, - 6, 12, 4, 20,? is 13.

Solution:

The given sequence is 3,-6,12,4,20,?

We need to find the next term of the sequence. If we observe the sequence we see that the terms are increasing and decreasing one after the other. To calculate the pattern of increase and decrease we can do the following.

3 - (-6) = 9

-6-12=-18

12-4=8

4-20=-16

If we ignore the negative sign we can observe that the difference between the consecutive numbers has a pattern.

the first difference is 9 and the next difference is twice that of the first one.

The third difference is one less than the first one and the fourth difference is twice that of the third one.

So by logic the next number should be one less than 8 that is,

8-1=7.

Since the pattern in the sequence is that of increase and decrease.

We need to subtract 7 from 20.

=20-7=13.

Therefore, the next term in the sequence has to be 13.