Question

我不知道

求這兩題

& 一等開級數前 項的總和S,三一2jz + ,則此等差級數的第 15 項為多禾講#.  5
(一435
(8)一61
(0一35
0一53                                                3
| 者一等差級數之奇數項和為一1980,偶數項和為一2190, 上由已和該等差多
共有 30 項 , 則此等差級數的首項為多少?
遙4
(8) 128
(C) 64

吃32

Answer 1

✨ 最佳解答 ✨

Ny-Ålesund

15^2 = 15的平方

a15 = S15 - S14
S15 = -2 × 15^2 + 15 = -435
S14 = -2 × 14^2 + 14 = -378
a15 = S15 - S14 = (-435) - (-378) = -57 #

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首項 = a、公差 = d
a + (a+2d) + (a+4d) + ... + (a+28d) = -1980 ...(1)
(a+d) + (a+3d) + (a+5d) + ... + (a+29d) = -2190 ...(2)
(2) - (1)
d + d + d + ... + d = -210
15d = -210, d = -14

(a + a+28d)×15÷2 = -1980
2a - 392 = -264
2a = 128, a = 64 #