The next term of the series made up of 2, 6, 12, 20, 30... has to be determined.

The numbers do not form an arithmetic series as 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8... the difference is not common. Also, the ratio of the terms is not common.

Looking at the difference between the terms it can be seen that 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10. The difference of the terms forms an arithmetic series with common difference 2.

This gives the next term of the series as 30 + 12 = 42

**The next term of the series made up of 2, 6, 12, 20, 30... is 42.**

Another way to look at it is to note that (2(n+1)) is the difference, where n is the sequence number of the value. So for n=1, 2(n+1)=4, for n=2, 2(n+1)=6, etc. So to find the next number in the sequence, simply multiply the sequence number + 1 by 2 and add that value to the value of the number at sequence number n; value of n+1 = 2(n+1) + value at n. So if the value of n=1 is 2, the next value should be 2+2(1+1) = 6. And it is! If n=2 and the value at 2 is 6, 6+2(2+1) = 6+6 = 12. Works again!

the next teram will be 42....as we first add 4 then 6 then 8 then 10 and now we will add 12.....2 is being added up to the previous adding subsequently...so 30 +12 will be 42...cheers...