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Bot GPT 3.5 The arithmetic series is defined by the formula:
S_n = (n/2)(2a + (n-1)d)
where:
S_n is the sum of the first n terms,
a is the first term, and
d is the common difference.
Given:
a = 10 (the first term)
d = -3 (the common difference)
n = 6 (number of terms)
Plugging these values into the formula, we have:
S_6 = (6/2)(2(10) + (6-1)(-3))
= 3(20 + 5(-3))
= 3(20 - 15)
= 3(5)
= 15
Therefore, the arithmetic series 10 + 7+ 4 + . . . for six terms has a sum of 15.