If you find it hard to find the 30th number, there, and since it takes time to count your way up, here is faster way to find it.

2 + 4 + 6 + 8 + 10 + 12
1st 2nd 3rd 4th 5th 6th

Just realise each number is twice the value of its position.

So the 30th number is: 30 × 2 = 60

Then apply the pairing method.

Alternatively,

Sum
= 2 + 4 + 6 + 8 + 10 + 12 + ... + 30th number

We can observe that for the first 6 numbers,

2 + 4 + 6 + 8 + 10 + 12
1st 2nd 3rd 4th 5th 6th

Factor out 2,

= 2 × (1 + 2 + 3 + 4 + 5 + 6)

From this we can clearly see that each number in the bracket is the same as its position.

So for the sum of the first 30 numbers, we know that the last number in the bracket is 30.

Sum = 2 × (1 + 2 + 3 + 4 + 5 + 6 +... + 30)

= (1 + 2 + 3 + 4 + 5 + 6 +... + 30)
+ (1 + 2 + 3 + 4 + 5 + 6 +... + 30)

Basically it's as good as saying we split each number equally into two parts.


This can be rearranged into:

(1 + 2 + 3 + 4 + 5 + 6 +... + 30)
(30+29+28+27+26 25+...+1)


We pair the numbers in the top bracket with the corresponding number in the bottom bracket.

1 + 30 = 31
2 + 29 = 31
3 + 28 = 31
...
15 + 16 = 31
16 + 15 = 31
...
28 + 3 = 31
29 + 2 = 31
30 + 1 = 31

We have two sets of the bracket, so we can get 30 pairs of 31.

Total = 31 × 30 = 930