Question

Last question please

Answer 1

Let's try an make a formula to make things easy.

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Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table:           6, 12, 18, 24, ...

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First think, how would you work out the 7th term in the 6th times table?

You would do 6 times 7.

So the formula for the 6th times table is:

6n     (where n is the term you want to find out)

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So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

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Now lets compare the 6 times table to Andrew's pattern:

6 times table:           6, 12, 18, 24,

Andrew's pattern:     3, 9, 15, 21,

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If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be:  6n - 3   (since it's the 6 times table but minus 3)

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We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = 117    (remember, replace the n with 20)

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Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table:       5, 10, 15, 20

Ben's pattern:       3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

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Now swap out the n for 20  (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = 98

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So Andrew's 20th term is 117, and Ben's 20th term is 98.

All we do now is subtract them to find the difference:

117 - 98 = 19

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Answer:

Ben's 20th term is smaller by 19!

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