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The sequence π π is an arithmetic sequence if π sub π plus one minus π sub π is equal to what.
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In this question, weβre given a sequence π π.
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And we need to determine the property that π sub π plus one minus π sub π will have, which will make this an arithmetic sequence.
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Thatβs the difference between consecutive terms.
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To do this, letβs start by recalling what we mean by an arithmetic sequence.
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We say that a sequence is an arithmetic sequence if the difference between any two consecutive terms in our sequence is constant.
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And another way of thinking about this is saying we add a constant value to the previous term to generate the next term.
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For example, in this sequence, we add four to generate the next term.
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And weβre almost ready to answer this question.
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However, letβs first recall what we mean by the notation π sub π plus one and π sub π.
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The notation π sub π means the value of the πth term in the sequence.
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For example, if we call our sequence one, five, nine, 13, 17, π sub π, then the second term in our sequence is five.
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So π sub two is equal to five.
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Similarly, π sub one is equal to one, since the value of the first term is one.
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This means the expression π sub π plus one minus π sub π is the difference between consecutive terms in our sequence.
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For example, in our example of an arithmetic sequence, one difference of successive terms is the second term minus the first term, which is five minus one.
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And this value is equal to four, because we found π sub two by adding four to π sub one.
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But this will be true for any two consecutive terms in our sequence, since the next term in our sequence is the previous term plus four.
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This will hold true for any arithmetic sequence.
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Any arithmetic sequence is one where the difference between consecutive terms is constant.
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And another way of saying this is π sub π plus one minus π sub π is constant for any integer value of π greater than or equal to one.