To find the 18th term of the given expression \( mn + 10 + 7(n-1) \), we need to first simplify the expression.
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Start with the expression: \[ mn + 10 + 7(n - 1) \]
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Simplify \( 7(n - 1) \): \[ 7(n - 1) = 7n - 7 \]
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Substitute this back into the expression: \[ mn + 10 + 7n - 7 \]
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Combine the constant terms: \[ = mn + 7n + (10 - 7) \] \[ = mn + 7n + 3 \]
Now, we rewrite the expression for the general term: \[ T(n) = mn + 7n + 3 \]
To find the 18th term (i.e., \( T(18) \)): \[ T(18) = m(18) + 7(18) + 3 \]
Calculate \( 7(18) \): \[ 7 \times 18 = 126 \]
Now substituting this back into the original expression for \( T(18) \): \[ T(18) = 18m + 126 + 3 \] \[ = 18m + 129 \]
Thus, the 18th term is: \[ \boxed{18m + 129} \]