Which term of the sequence 18,12,8,.... is (512/729)? (Geometric Progression) The books shows that the answer is 9th but I’m getting 10th?
回答 (2)
2018-08-10 4:19 pm
First term, a = 18
Common ratio, r = 12/18 = 8/12 = 2/3
The nth term:
a rⁿ⁻¹ = 512/729
18 × (2/3)ⁿ⁻¹ = 512/729
(2/3)ⁿ⁻¹ = (512/729) × (1/18)
(2/3)ⁿ⁻¹ = 256/6561
(2/3)ⁿ⁻¹ = 2⁸/3⁸
(2/3)ⁿ⁻¹ = (2/3)⁸
n - 1 = 8
n = 9
It is the 9th term.
Common ratio, r = 12/18 = 8/12 = 2/3
The nth term:
a rⁿ⁻¹ = 512/729
18 × (2/3)ⁿ⁻¹ = 512/729
(2/3)ⁿ⁻¹ = (512/729) × (1/18)
(2/3)ⁿ⁻¹ = 256/6561
(2/3)ⁿ⁻¹ = 2⁸/3⁸
(2/3)ⁿ⁻¹ = (2/3)⁸
n - 1 = 8
n = 9
It is the 9th term.
2018-08-13 6:50 pm
18, 12, 8, 16/3, ...
an = 2^n 3^(3 - n)
512/729 = 2^n 3^(3 - n)
Integer solution:
n = 9
18, 12, 8, 16/3, 32/9, 64/27, 128/81, 256/243, 512/729, ...
(512/729) is the 9th term.
an = 2^n 3^(3 - n)
512/729 = 2^n 3^(3 - n)
Integer solution:
n = 9
18, 12, 8, 16/3, 32/9, 64/27, 128/81, 256/243, 512/729, ...
(512/729) is the 9th term.
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