# What is the next term of the series 2, 6, 12, 20, 30...

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

academy633 | College Teacher | (Level 1) Salutatorian

Posted on

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!

tusharbhatia | Student, Grade 10 | eNotes Newbie

Posted on

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...