GCSE mathematics ‘common difference’ arithmetic sequence questions appear on many exam papers. This is where the same number is added, or subtracted, each time. For instance the sequence 12, 16, 20, 24, 28 …. has a common difference of add 4 …… or 16, 8, 0, -8, -16 has a common difference of subtract 8.

You’re usually asked to create a formula for ‘the nth term’ and use it to calculate a value.

There is another type, called a geometric sequence, where each term is multiplied or divided. More about this one in a future post :-).

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Arithmetic sequences can be quite useful to calculate real life word problems. A good example would be:

“A cinema has seating arranged as follows:

1st row 15 seats, 2nd row 20 seats, 3rd row 25 seats, 4th row 30 seats.

How many seats are there in the 20th row?”

You might like to view the video if a little unsure with these steps. The question centres around the ‘common difference’ – in this case add 5 – and the zero term. In this case the 1st term is 15 and each of the next terms are calculated by adding 5. Therefore the ‘zero term’ is 10.

The formula you need is now:

nth term = 5n + 10

To calculate the 20th row we can just ‘plug in’ the numbers, so:

20th term = (5 x 20) + 10

20th term = 110

There are 110 seats on the 20th row.

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**Just a thought:**

By working through a couple of examples you might notice that a rule could be created for working out totals. If you calculate the average of the first and last terms in a sequence, and then multiply by the number of terms, you get the total.

Hmmm. Saying this mathematically:

Total = ((first term + last term) / 2) and then multiply by the number of terms.

Tidied up this would be written as _{Sn} = ½n(a_{1} + a_{n})

So, for the 20 row cinema the average of first (15) and last (110) term is 62.5. Multiply this by 20 terms = 1250. So the cinema has 1250 seats.

Watch on YouTube

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