SOLUTION: Find the sixth term of the sequence 2, 6, 12, 20, 30,...

Algebra.Com
Question 877326: Find the sixth term of the sequence
2, 6, 12, 20, 30,...
Found 2 solutions by AnlytcPhil, josgarithmetic:
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
2, 6, 12, 20, 30,...

 2 = 1×2
 6 = 2×3
12 = 3×4
20 = 4×5
30 = 5×6

So the next term is 6×7 = 42.

The nth term is 

an = n(n+1)

Edwin
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
A clear relationship is happening over the differences between successive terms.

These are those differences, as a list: 4, 6, 8, 10,...
The next difference should be 12. This will be the term 30+12=42.
The next difference should be 14. This will give the term 42+14=56.
RELATED QUESTIONS

find the sixth term of the geometric sequence... (answered by richard1234)
The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th... (answered by ikleyn,Fombitz)
Find the common difference of the arithmetic sequence whose second term is 6 and sixth... (answered by Fombitz)
Find the sixth term in the sequence in which a^4=20 and r=-3 (answered by josgarithmetic,MathTherapy)
Find the fifth term of a geometric sequence in which the fourth term is 4, the sixth term (answered by josgarithmetic)
What is the nth term rule of the quadratic sequence below? 6 , 12 , 20 , 30 ,... (answered by ikleyn,Edwin McCravy)
Find the sixth term of the geometric sequence 1/2, 1/3, 2/9 Is 32/729... (answered by jim_thompson5910)
the third term of a geometric sequence is 4 and the sixth term is 32/27. find the nth... (answered by MathLover1)
The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the... (answered by josgarithmetic,greenestamps)