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 <u>7</u>th term in the <u>6</u>th times table?
You would do <u>6</u> times <u>7</u>.
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 = <u>117</u> (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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<u>Now swap out the n for 20</u> (to get the 20th term):
20th term = 5 x 20 - 2 = 100 - 2 = <u>98</u>
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So Andrew's 20th term is <u>117</u>, and Ben's 20th term is <u>98</u>.
All we do now is subtract them to find the difference:
117 - 98 = <u>19</u>
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Answer:
Ben's 20th term is smaller by 19!
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