Geometric sequence question

2008-10-12 7:58 pm

The sum of three numbers is 9 and their product is -216. Find the three numbers if they form a geometric sequence.
(please show detailed steps)

回答 (1)

Uncle Michael

2008-10-12 9:07 pm

✔ 最佳答案

The three number form a geometric sequence.
Let a, ar and ar2 be the three numbers.

a + ar + ar2 = 9 ...... (1)
a(ar)(ar2) = -216 ...... (2)

(2):
a3r3 = -216
(ar)3 = (-6)3
ar = -6
r = -6/a ...... (3)

Put (3) into (1):
a + a(-6/a) + a(-6/a)2 = 9
a - 6 + 36/a = 9
Multiply each term on both sides by a:
a2 - 6a + 36 = 9a
a2 - 15a + 36 = 0
(a - 3)(a - 12) = 0
a = 3 or a = 12

When a = 3:
r = -6/3
r = -2
ar = 3 x (-2)
ar = -6
ar2 = 3 x (-2)2
ar2 = 12

When a = 12
r = 6/(-12)
r = (-1/2)
ar = 12 x (-1/2)
ar = -6
ar2 = 12 x (-1/2)2
ar2 = 3

Ans: The three numbers are 3, -6, 12.
=

👍 0 👎 0