Find the tenth term of the geometric sequence rad 3, 1, rad 3 / 3, ...
Five stars for the first person who explains it well!
goooooooooo :)
Five stars for the first person who explains it well!
goooooooooo :)
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The first term, a[1] of this sequence is sqrt(3), the proportion factor is k = 1/sqrt(3)
So, the second term a[2] = ka[1], the 3rd term, a[3] = (k^2)a[1], the 4th term, a[4] = (k^3)a[1], etc
So, the 10th term a[10] = (k^9)a[1] = (1/sqrt(3)^9)(sqrt(3)) = 1/sqrt(3)^8 = 1/3^4 = 1/81.
So, the second term a[2] = ka[1], the 3rd term, a[3] = (k^2)a[1], the 4th term, a[4] = (k^3)a[1], etc
So, the 10th term a[10] = (k^9)a[1] = (1/sqrt(3)^9)(sqrt(3)) = 1/sqrt(3)^8 = 1/3^4 = 1/81.