$\"\"$

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The 10th term of the sequence is 84. The 21st term of the sequence is 161.

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

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Case 1:-

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$\"\"$ (Substitute n = 10)

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$\"\"$ (Substitute $\"\"$ )

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

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Case 2:-

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$\"\"$ (Substitute n = 21)

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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 11)

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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 subtraction property of equality: a = b then $\"\"$ .

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$\"\"$ (Subtract 63 from each side)

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

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Find the nth term of the sequence, substitute $\"\"$ and d = 7.

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$\"\"$

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Distribute terms using distributive property: $\"\"$ .

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$\"\"$

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

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