Sequences

Hello, and welcome to Myriora Maths! Three, seven, eleven, fifteen. What comes next? And what would the hundredth number be? Let's find the pattern, and a rule for any position.

Each number is four more than the one before. That's the term-to-term rule: add four. So the next terms are nineteen, then twenty-three.

But adding four a hundred times is slow. So let's number the positions: one, two, three, four. The terms are three, seven, eleven, fifteen.

The terms go up by four, just like the four times table. The four times table is four, eight, twelve, sixteen. Each term is one less. So the rule is four n take away one, where n is the position.

Now jump straight to any term. The tenth term is four times ten, take away one: thirty-nine. The hundredth term is four hundred take away one: three hundred and ninety-nine!

Let's try one together. Five, eight, eleven, fourteen. What's the term-to-term rule, and what comes next? Say it out loud!

Each term is three more: add three. So the next term is seventeen!

Here's a question that catches lots of people. What is the tenth term of three, seven, eleven? Some people start at three and add four ten times, and get forty-three. But from the first term to the tenth there are only nine jumps. Three add nine fours is thirty-nine!

Your turn! Two, seven, twelve, seventeen. What is the twentieth term? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! The terms go up by five, so look at the five times table. Each term is three less than five n. So the rule is five n take away three. The twentieth term is a hundred take away three: ninety-seven!

Quick review. The term-to-term rule tells you how to get from one term to the next. The position-to-term rule, like four n take away one, jumps straight to any term. Compare with a times table to find it. And count the jumps carefully. See you next time!