geometric sequence
2011-07-28 5:24 am
Given a geometric sequence whose sum of the first 10 terms is 2 and whose sum from the 11st to 30th term is 12, find the sum from the 31st and 60th term
回答 (1)
2011-07-28 5:49 am
✔ 最佳答案
Let S(n) be the sum of the first n term.S(10) = 2S(30) = S(10) + 12 = 14Let r be the common ratio :S(30) = S(10) + (r¹º)S(10) + (r²º)S(10)14 = 2 + 2r¹º + 2r²ºr²º + r¹º - 6 = 0(r¹º - 2) (r¹º + 3) = 0r¹º = 2 or r¹º = - 3(rejected)The sum from the 31st and 60th term= S(60) - S(30)= (r³º) S(30) - S(30)= 2³ (14) - 14= 98
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