(a) the first term and the common difference
(b) the sum of the first 30 terms
of the series.
更新1:
求 : 完整步驟 + 答案
S6 Maths. Sequences&Series 一題
2013-11-30 5:00 am
Given that the sum of the first 10 terms of an arithmetic series is 310, and the sumfrom the 6th term to the 13th term is 408, find
(a) the first term and the common difference
(b) the sum of the first 30 terms
of the series.
(a) the first term and the common difference
(b) the sum of the first 30 terms
of the series.
回答 (2)
2013-11-30 7:08 am
✔ 最佳答案
first term = anth term = a + (n-1)d
Sum of n terms = {(a) + [a+(n-1)d]}(n)/2
sum of the first 10 terms of an arithmetic series is 310 gives
(a + a + 9d)(10)/2 = 310
2a + 9d = 62 ................... (1)
6,7,8,9,10,11,12,13 6th term to 13th term are 8 terms
6th term is a + 5d
13th term is a + 12d
[(a + 5d) + (a + 12d)](8)/2 = 408
(2a + 17d) = 102 ............ (2)
(2) - (1) ===> 8d = 40
d = 5
sub into (1) ==> 2a + 9(5) = 62
2a = 62 - 45 = 17
a = 8.5
(b) the sum of the first 30 terms
Sum = (a + a+29d)(30)/2
= [8.5 + 8.5 + (29)(5)](30)/2 = 2430
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厺及叛匕匄勴
厺及叛匕匄勴
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https://hk.answers.yahoo.com/question/index?qid=20131129000051KK00145