Using Excel/TI calclulators to determine the pattern for numbers 3, 6, 10?

Question

I know that it is a combination, and can be solved using the formula, but how does a graph or technology tell you that it really is?

Answer 1

I'll explain how to do it in Excel.

In one column, put the numbers 1, 2, 3
In the second column, put the pattern numbers 3, 6, 10

Now select the 6 cells and click the 'Chart Wizard' (or Insert > Chart). Pick an X, Y scatter with straight lines.

On your graph, right-click on the line and choose 'Add Trendline'. I'd pick a 2nd order polynomial. Then click on the 'Options' tab and choose 'Display equation on chart'.

In this example you end up with:
y = 0.5x² + 1.5x + 1

Check the pattern by putting in additional numbers:
x = 4 --> y = 8 + 6 + 1 = 15
x = 5 --> y = 12.5 + 7.5 + 1 = 21
etc.

So this gives you a pattern of 3, 6, 10, 15, 21, 27, etc.