karma35 said:

Took about a minute. :-) Here's are the steps to solving it fast:

7 + 13 + 19 + ... + 673

First recognize that the sequence can be represented as follows:

= (6*1 + 1) + (6*2 + 1) + (6*3 + 1) + ... + (6*112 + 1)

Now bring out all of the "+1" terms, which equal 112.

= 6*1 + 6*2 + 6*3 + ... + 6*112 + 112

Now factor out the sixes:

= 6 * (1 + 2 + 3 + ... + 112) + 112

Now it looks tedious, but it's not if you know the "trick" to adding a long series of numbers:

= 6 * ((112 +1) + (111 + 2) + (110 + 3) + ... + (57 + 56)) + 112

Notice that all of the parenthesized terms add up to 113, and there are exactly 56 of them. So the long tedious addition reduces to a simple multiplication:

= 6 * (113 * 56) + 112

And now just type them in to a calculator:

= 38080

:-)

---