Number Sequence - help me please?

[mini]

I was just going to finish off my revision when I came to a question, which I haven no idea how to tackle. It might be sooo very easy, i don't know.. i just have no idea what to do, please help, thank you! x 1) Work out the difference between the nth number and the (n+1)th number. Give your answer as simply as you can in terms of n. The sequence: 2,6,12,20 (Note: In the previous question, it asked me to find the nth term of the sequence and that I found to be n^2 + n ...)ok.. i found out that the answer is: 2n + 2 or 2(n+1) ... but i still don't get how to work it out. Thanks for all your help - i'm trying to understand it.. hopefully it'll click into my head aaanny second now. =)

[thefreevariable]

Looks to me like f(1) = 2, f(n+1) = f(n) + 2(n+1). This is the sequence in recursive notation. I chose to do it recursively so that we would have an explicit relationship between f(n+1) and f(n). Subtracting, we have f(n+1) - f(n) = 2(n+1). So 2(n+1) is the difference between the (n+1)th number and the (n)th number.

[Justin B]

Just look at the difference between the numbers.2->6 is 46->12 is 612->20 is 8So since it's counting up with even numbers, 2*n is a good candidate. A good place to start would be seeing if you can add 2*n to the previous number to get the next answer (or n = (n-1) + 2*n)Let's see if we can rewrite the sequence in those terms:f(2) = f(n-1) + 2^n => 2 + 2*2 = 6 f(3) = f(n-1) + 2^n => 6 + 2*3 = 12Looks like your answer is:f(1) = 2f(n) = f(n-1) + 2*n

[Aidas]

The difference between first and second - 4, second and third - 6, 3 and 4 - 8, so the difference between n and n+1 will be 2*(n+1)

[TychaBrahe]

OKTerm Value 1 2 2 6 3 12 4 20 I notice that the value = n*(n+1)So the next term, the 5th term = 5 * 6 = 30.