\"\"

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The 63rd term of the sequence is 237. The 90th term of the sequence is 75.

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Apply nth term of the arithmetic sequence formula: \"\".

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Case 1:-

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\"\"                         (Substitute n = 63)

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\"\"                       (Substitute \"\")

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\"\"                                 (Subtract: \"\")

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Case 2:-

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\"\"                         (Substitute n = 90)

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\"\"                          (Substitute \"\")

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\"\"                                   (Subtract: \"\")\"\"

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\"\" -------------->   (Equation 1)

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\"\"   -------------->   (Equation 2)

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Subtracting the equations (2) from (1).

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\"\"

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Apply division property of equality: a = b then \"\".

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\"\"                                 (Divide each side by 27)

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\"\"                                        (Cancel common terms)

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\"\"                                               (Divide: \"\")\"\"

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Find the first term of the sequence, substitute \"\" in \"\".

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\"\"

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\"\"                                  (Multiply: \"\")

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Apply addition property of equality: a = b then \"\".

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\"\"             (Add 372 to each side)

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\"\"                                             (Add: 237 + 372 = 609)\"\"

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Find the nth term of the sequence, substitute  \"\" and \"\".

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\"\"

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Distribute terms using distributive property: \"\".

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\"\"

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\"\"                              (Product of two same signs positive)

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\"\"                                    (Add: 609 + 6 = 615)\"\"

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The nth term of the arithmetic sequence equation is \"\".