Adding any run of numbers

Hello, and welcome to Myriora Maths! What is five, plus eight, plus eleven, all the way up to thirty-eight, going up in threes? It looks scary. But there's a quick way!

Remember adding one to a hundred? We paired the first number with the last, and every pair made the same total. That works for any list that goes up by the same step each time.

Let's pair them. Five and thirty-eight make forty-three. Eight and thirty-five: forty-three. Eleven and thirty-two: forty-three again!

Now, how many numbers are there? Find the gap from first to last: thirty-eight take five is thirty-three. Divide by the step: thirty-three divided by three is eleven steps. And there's one more number than steps: twelve numbers!

So, first plus last, times how many, divided by two. Forty-three times twelve, divided by two, is two hundred and fifty-eight!

A common mistake is counting the numbers wrongly. Thirty-three divided by three is eleven, but that's the steps. There are twelve numbers, not eleven.

Your turn! Add up four, plus nine, plus fourteen, all the way to forty-nine. You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Four plus forty-nine is fifty-three. There are ten numbers. Fifty-three times ten, divided by two, is two hundred and sixty-five!

Quick review. Pair the first number with the last. Count the numbers: the gap, divided by the step, plus one. Then multiply, and halve. See you next time!