To find the 62nd term of the arithmetic sequence given by \(-27, -21, -15, \ldots\), we first identify the first term \(a_1\) and the common difference \(d\).
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The first term \(a_1\) is: \[ a_1 = -27 \]
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The common difference \(d\) can be calculated by subtracting the first term from the second term: \[ d = -21 - (-27) = -21 + 27 = 6 \]
Now, the formula for the \(n\)-th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1)d \]
We need to find the 62nd term (\(n = 62\)): \[ a_{62} = a_1 + (62 - 1)d \] Substituting the values we have: \[ a_{62} = -27 + (61)(6) \] Calculating \(61 \times 6\): \[ 61 \times 6 = 366 \] Now substitute back: \[ a_{62} = -27 + 366 = 339 \]
Thus, the 62nd term \(a_{62}\) is: \[ \boxed{339} \]