Insert five numbers between 0.125 and 8 so that the seven numbers form a geometric sequence.?
回答 (5)
2019-02-20 11:14 am
Geometric sequence: 0.125, T(2), T(3), T(4), T(5), T(6), 8
Let r be the common ratio of the geometric sequence.
The first term, a = 0.125
The seventh term, T(7) = 8
The seventh term:
T(7) = a r⁶
8 = 0.125 r⁶
r⁶ = 8/0.125
r⁶ = 64
r⁶ = 2⁶
r = 2
T(2) = 0.125 × 2 = 0.25
T(3) = 0.25 × 2 = 0.5
T(4) = 0.5 × 2 = 1
T(5) = 1 × 2 = 2
T(6) = 2 × 2 = 4
Hence, the inserted 5 numbers are 0.25, 0.5, 1, 2 and 4.
Let r be the common ratio of the geometric sequence.
The first term, a = 0.125
The seventh term, T(7) = 8
The seventh term:
T(7) = a r⁶
8 = 0.125 r⁶
r⁶ = 8/0.125
r⁶ = 64
r⁶ = 2⁶
r = 2
T(2) = 0.125 × 2 = 0.25
T(3) = 0.25 × 2 = 0.5
T(4) = 0.5 × 2 = 1
T(5) = 1 × 2 = 2
T(6) = 2 × 2 = 4
Hence, the inserted 5 numbers are 0.25, 0.5, 1, 2 and 4.
2019-02-20 11:09 am
0.125 , a , b , c , d , e , 8
0.125 * r^6 = 8
r^6 = 8 / (1/8)
r^6 = 64
r = 2
0.125 , 0.125 * 2 , 0.125 * 2^2 , 0.125 * 2^3 , 0.125 * 2^4 , 0.125 * 2^5 , 8
0.125 , 0.25 , 0.5 , 1 , 2 , 4 , 8
0.125 * r^6 = 8
r^6 = 8 / (1/8)
r^6 = 64
r = 2
0.125 , 0.125 * 2 , 0.125 * 2^2 , 0.125 * 2^3 , 0.125 * 2^4 , 0.125 * 2^5 , 8
0.125 , 0.25 , 0.5 , 1 , 2 , 4 , 8
2019-02-20 12:16 pm
0.125, 0.25, 0.5, 1, 2, 4, 8
an = 2^(n - 4)
an = 2^(n - 4)
2019-02-20 12:07 pm
0.125, 0.250, 0.500, 1, 2, 4, 8.
2019-02-20 11:09 am
Hint - 0.125 = 1/8.
收錄日期: 2021-05-01 22:26:20
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20190220030739AAV3EXX