### Second Common Differences can be a bit complicated.

The SHARP EL-535 can be very useful to help you figure out the formula and also to check whether your answers are right.

Let’s do an example: You are given the pattern 3, 7, 15…

### On your calculator press:

1 (For stat) and then 2 for Quad (this selects a quadratic pattern, or second common differences pattern). (Make sure you have cleared all the previous data by pressing )

You have the first three terms in the pattern.

To enter the data press 1 (for term one) and then 3 (the value of the first term) and

Then enter the second term: press 2 and then 7 .

Finally enter the third term: press 3 and then 15 .

Now if you look at the cover of your calculator From MODE SELECT:

you have normal, then stat, the SD and then LINE. Next to line is QUAD with the formula y = a +bx +cx^{2}. You will notice that the c and a have switched places in this formula compared to the formula you usually use.

To find the y intercept (in this formula – a) press . This will give you 3.

To find the coefficient of x (b) press . This will give you -2.

Finally to get the coefficient of x^{2} (c) press . This will give you 2.

So your formula for the pattern is 2x^{2} -2x +3.

NB!!!! Remember – you still need to show your working out – but it is a quick way to check your answer and make sure you have those marks in the bag 🙂

Now – even cooler, once you have your formula (although you can do this without working it out) you can find the term value given the term’s position and you can find the term’s position given the term value.

E.g. What is the value of the 6th term?

On your calculator press 6 and the calculator will give you 63. (Subs it into your formula to see that this is true).

E.g. What is the value of n if Tn = 183.

On your calculator press 183 and the calculator will give you x = 10 or -9 – we know that n cannot be negative so n is 10.

Again, remember this is just a quick way to check your answers – you still need to show your working out to get the marks.