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Find the next term in the sequence: twenty-eight thirty-seven forty-six fifty-five sixty-four.
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So we’ve been given five terms in a sequence.
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The first term is twenty-eight, the second term is thirty-seven, the third term forty-six, the fourth term is fifty-five, and the fifth term is sixty-four.
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Now the fact that it’s been called a sequence tells us that there must be some sort of pattern that takes you from one number to the next number, some sort of common pattern that’s going on.
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Well if I look at the first term and the second term, twenty-eight and thirty-seven, if I add nine to twenty-eight, I get thirty-seven.
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And also if I add nine to thirty-seven, I get forty-six.
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If I add nine to forty-six, I get fifty-five.
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And if I add nine to fifty-five, I get sixty-four.
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So my pattern is that, to get from one term to the next term, I add nine.
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So to find the next term in my sequence, the sixth term, I need to add nine to sixty-four.
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And that will give me seventy-three.
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So the answer is seventy-three.
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Now just a little bit of terminology before we go, in this kind of sequence where you add a constant number to each term to get the next term is called an arithmetic sequence.