To find the 21st term \( a_{21} \) in the arithmetic sequence given by the numbers \( 10, 7, 4 \), we first need to identify the first term and the common difference.
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Identify the first term \( a_1 \): \[ a_1 = 10 \]
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Calculate the common difference \( d \): The common difference can be found by subtracting the first term from the second term: \[ d = a_2 - a_1 = 7 - 10 = -3 \]
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Use the formula for the \( n \)-th term of an arithmetic sequence: The formula for the \( n \)-th term \( a_n \) of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1)d \] Substituting \( n = 21 \), \( a_1 = 10 \), and \( d = -3 \): \[ a_{21} = 10 + (21 - 1)(-3) \] \[ = 10 + 20 \times (-3) \] \[ = 10 - 60 \] \[ = -50 \]
Thus, the 21st term \( a_{21} \) of the sequence is \( -50 \).