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Find 𝑎, 𝑏, and 𝑐 given the arithmetic sequence 𝑎, 44, 𝑏, 64, 𝑐.
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In an arithmetic sequence, the difference between one term and the next is a constant.
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If we think about it in terms of a number line, the distance between every value is constant.
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How do we get from 44 to 64?
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We add 20.
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But that is two spaces in the sequence.
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And that means that each space in the sequence is plus 10.
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The sequence increases by 10 units every time.
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Value 𝑏 would be 10 units more than 44.
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𝑏 equals 54.
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Value 𝑐 is 10 units more than 64, which is 74.
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And value 𝑎 is 10 units less than 44, 34.
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In this sequence, 𝑎 equals 34, 𝑏 equals 54, and 𝑐 equals 74.