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The first and last terms of an arithmetic sequence are negative 55 and 209, respectively.
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There are 21 terms between the first and last terms.
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Find the list of these intermediate terms.
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We begin by recalling that an arithmetic sequence has a common difference between consecutive terms.
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The general term or πth term in an arithmetic sequence can be found using the formula π sub π is equal to π sub one plus π minus one multiplied by π, where π sub one is the first term in the sequence and π is the common difference.
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In this question, we are told that the first term in the sequence is negative 55.
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The last term in the sequence is 209.
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As there are 21 terms between them, there are 21 plus two or 23 terms altogether in the sequence.
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This means that the last term 209 is the 23rd term.
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We can substitute these values into the general formula to calculate the common difference π.
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The 23rd term is equal to negative 55 plus 23 minus one multiplied by π.
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And as this term equals 209, we have 209 is equal to negative 55 plus 22π.
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Adding 55 to both sides of this equation, we have 22π is equal to 264.
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We can then divide through by 22, giving us an answer for the common difference π equal to 12.
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As the first term was negative 55, we need to add 12 to this to find the next term.
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This is equal to negative 43.
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Repeating this process, the next two terms are negative 31 and negative 19.
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We know that the last term in the sequence is 209.
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As the common difference is 12, the term before this will be 12 less than 209.
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This is equal to 197.
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The entire sequence is negative 55, negative 43, negative 31, negative 19, and so on, up to 197 and 209.
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This is not the final answer, however, as we were just asked to list the intermediate terms.
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This is the list of terms between the first and last term.
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The answer to this question is the sequence of numbers negative 43, negative 31, negative 19, and so on, all the way up to 197.