Final answer:
The partial sum S₁₂ of the arithmetic sequence {38, 31, 24, 17, ...} is -6, calculated using the formula for the sum of the first n terms of an arithmetic sequence.
Step-by-step explanation:
To find the partial sum S₁₂ for the given sequence {38, 31, 24, 17, ...}, we first notice that this is an arithmetic sequence where each term is 7 less than the previous one. Therefore, the common difference d is -7. To find the 12th term, we use the nth term formula for an arithmetic sequence: a_n = a_1 + (n-1)d. Substituting the values, we get a₁₂ = 38 + (12-1)(-7) = 38 - 77 = -39.
Now, to find the partial sum S₁₂, we use the sum formula for the first n terms of an arithmetic sequence: S_n = n/2(a_1 + a_n). With our values, this becomes S₁₂ = 12/2(38 - 39) = 6(-1) = -6. Thus, the partial sum of the first 12 terms is -6.