F5 math problems
2007-09-25 3:15 am
The infinite sum of a geometric sequence is 4 and the infinite sum of the cubes of its terms is equal to 192.Find the first term and the common ratio.
回答 (1)
2007-09-25 3:24 am
✔ 最佳答案
a + ar + ar^2 +...S = a/(1-r) = 4 -----------(1)
a^3 + (ar)^3 + (ar^2)3 +...
S(cube) = a^3/(1-r^3) = 192 --------(2)
sub (1) into (2)
[4(1-r)]^3 = 192 (1-r^3)
(1 - r)^2 = 3 (1+r+r^2)
1 - 2r +r^2 = 3 + 3r +3r^2
2r^2 +5r + 2 = 0
(2r + 1) (r+2) = 0
r = -1/2 or -2 (reject r = -2)
r = -1/2
r = -1/2 sub into (1)
a /(1-(-1/2)) = 4
a = 6
參考: My calculation
收錄日期: 2021-04-18 23:25:02
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