Question

Here are the first five terms of the sequence

0 2 6 12 20
find an expression, in terms of n, for the nth term of this sequence

Answer 1

`n(n+1)`

Explanation:

Given

the nth term of the sequence 0,2,6,12,20 can be expressed as

There is a pattern for the sequence 2,4,6,8,10….. So in this case the nth term will be 2 n

Now n = 0 1 2 3 4

So n(n + 1)/2 = 1,3,6,10,15

We can see from this the required sequence is double the one which is nth term. Therefore the nth term for the sequence will be 2 n (n + 1) / 2 = n(n + 1).