Expert: Sherry Wallin - 7/29/2010

Question
i have a problem answering this series: 1,2,6,42,1806,___ can you help me find the next series and how to get it?thanks!

Answer
Hi Ghing~

This is a sequence of numbers. If you look closely for a pattern you will see that the first number 1 is squared and then added to 1:
1^2 + 1 = 2
2^2 + 2 = 6
6^2 + 6 = 42
42^2 + 42 = 1806
1806^2 + 1806 = 3263442

another way to look at this is to realize that 1^2 + 1 is n^2 + n = n(n+1)
check it out and see if this works:
let n = 1 then 1(1+1) = 2
let n = 2 the 2(2+1) = 6
let n = 6 then 6(6+1) = 42
let n e 42 then 42(42+1) = 1806  and
let n = 1806 then 1806(1806 + 1) = 3263442

Now all YOU have to figure out is how the n's are generated. Notice we didn't have an
n = 3,4, or 5 when we needed 6.


Think about this for a bit and let me know if you still need help.

Math Prof