QuestionDecember 16, 2025

Find the partial sum. 38,31,24,17,ldots ;S_(12)

Find the partial sum. 38,31,24,17,ldots ;S_(12)
Find the partial sum.
 38,31,24,17,ldots ;S_(12)

Solution
4.2(179 votes)

Answer

-6 Explanation 1. Identify sequence type and parameters The sequence decreases by 7; it's arithmetic with a_1 = 38, d = -7. 2. Use partial sum formula for arithmetic sequence The sum of first n terms: S_n = \frac{n}{2}(2a_1 + (n-1)d). 3. Substitute values S_{12} = \frac{12}{2}[2 \times 38 + (12-1)(-7)] 4. Simplify inside brackets 2 \times 38 = 76, (12-1) = 11, 11 \times (-7) = -77, so 76 + (-77) = -1. 5. Calculate final sum S_{12} = 6 \times (-1) = -6

Explanation

1. Identify sequence type and parameters<br /> The sequence decreases by $7$; it's arithmetic with $a_1 = 38$, $d = -7$.<br />2. Use partial sum formula for arithmetic sequence<br /> The sum of first $n$ terms: $S_n = \frac{n}{2}(2a_1 + (n-1)d)$.<br />3. Substitute values<br /> $S_{12} = \frac{12}{2}[2 \times 38 + (12-1)(-7)]$<br />4. Simplify inside brackets<br /> $2 \times 38 = 76$, $(12-1) = 11$, $11 \times (-7) = -77$, so $76 + (-77) = -1$.<br />5. Calculate final sum<br /> $S_{12} = 6 \times (-1) = -6$
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