geometric sequence question?

👨🏻‍🏫 學術台數學

[匿名]

2017-02-18 10:12 pm

find the value of the 10th term of this geometric progression
2√3, 12, 23√3, 144, 288√3....

what is the answer?

a) 576√3
b)20736
c)20736√3
d)248832

-i found out that the sequence is multiplied by 2√3 but im unable to find the answer-

更新1:

so what is the answer? a,b,c,d it was a multiple choice question and those 4 were the only options

回答 (2)

micatkie

2017-02-18 10:29 pm

✔ 最佳答案

The geometric progression should be :
2√3, 12, 24√3, 144, 288√3.......

First term, a = 2√3
common reatio, r = 12/2√3 = 24√3/12 = 144/24√3 = 288√3/144 = 2√3

The 10th term
= a r^9
= (2√3) × (2√3)^9
= (2√3)^10
= 2^10 × (√3)^10
= 1024 × [3^(1/2)]^10
= 1024 × 3^5
= 1024 × 243
= 248832

The answer: d) 248832

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[匿名]

2017-02-18 10:21 pm

(Oops! 24√3 , not 23√3)
Yes, you have the ratio correctly.
It should be no trouble to find the 10th term -- 9 terms froward from the first.
t_10 = t_1 * r^9
= 2√3 * (2√3)^9
= (2√3)^10 . . . . . . . = 12^5, if you prefer
= 2^10 * 3^5
= 1024 * 243
= 128832

👍 1 👎 1

用戶55769

2017-02-19 12:36 am

2√3, 12, 24√3, 144, 288√3....
an = 2^n 3^(n/2)
10th term is = 248832.
Answer choice:
d) 248832

參考: http://www.wolframalpha.com/input/?i=2%E2%88%9A3,+12,+24%E2%88%9A3,+144,+288%E2%88%9A3,+...

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