1. The general term Tn of a geometric sequence is 5^n-3. Find the sum of the first 5 terms in the sequence.
2. a^3/2 x a^3 x a^6 x a^12 x ... x a^192=
3. Consider the geometric sequence 2,6,18,54,162,.... Find the sum of the first 20 terms of the sequence 3,7,19,55,163,...
ans:
1) 781/25
2) a^765/2
3) 3^20+19
pls show clear steps.thanks!
geometric sequence
2011-10-28 3:20 am
回答 (1)
2011-10-28 3:33 am
✔ 最佳答案
1 T(1) + T(2) + T(3) + T(4) + T(5)= 1/25 + 1/5 + 1 + 5 + 25
= 31 + 6/25
= 781/25
2 (3/2) + 3 + 6 + ... + 192
= (3/2)(2^8 - 1)/(2 - 1)
= 765/2
a^3/2 x a^3 x a^6 x a^12 x ... x a^192
= a^(765/2)
3 3 + 7 + 19 + 55
= 2 + 6 + 18 + ... + 3^19 + 20
= 2(3^20 - 1)/(3 - 1) + 20
= 3^20 + 19
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https://hk.answers.yahoo.com/question/index?qid=20111027000051KK00638