# How do you find the 12th partial sum of the arithmetic sequence #4.2, 3.7, 3.2, 2.7,...#?

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To find the 12th partial sum of the arithmetic sequence (4.2, 3.7, 3.2, 2.7, \ldots), we can use the formula for the sum of the first (n) terms of an arithmetic sequence:

[ S_n = \frac{n}{2}(a_1 + a_n) ]

where:

- (S_n) is the sum of the first (n) terms,
- (a_1) is the first term of the sequence, and
- (a_n) is the (n)th term of the sequence.

Given that the first term (a_1 = 4.2), the common difference (d = 3.7 - 4.2 = -0.5), and we want to find the 12th partial sum (S_{12}), we can plug these values into the formula:

[ S_{12} = \frac{12}{2}(4.2 + a_{12}) ]

[ S_{12} = 6(4.2 + (12 - 1)(-0.5)) ]

[ S_{12} = 6(4.2 + 11(-0.5)) ]

[ S_{12} = 6(4.2 - 5.5) ]

[ S_{12} = 6(-1.3) ]

[ S_{12} = -7.8 ]

So, the 12th partial sum of the given arithmetic sequence is (-7.8).

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