Mystery 7 7 th Term

Algebra Level 2

In the sequence below, what is the 7th term?

1 , 1 2 , 2 9 , 3 32 , 24 625 , 5 324 , ? \large 1, \ \frac{1}{2}, \ \frac{2}{9}, \ \frac{3}{32}, \ \frac{24}{625}, \ \frac{5}{324}, \ \boxed{\text{?}}

Note: The answer should be rounded up to the ten-millionths.


The answer is 0.0061199.

Kaizen Cyrus by Kaizen Cyrus , 18, Philippines

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1 solution

Chew-Seong Cheong
Feb 11, 2019

The n n th term is given by a n = ( n − 1 ) ! n n − 1 a_n = \dfrac {(n-1)!}{n^{n-1}} . Therefore a 7 = 6 ! 7 6 = 720 117649 ≈ 0.0061199 a_7 = \dfrac {6!}{7^6} = \dfrac {720}{117649} \approx \boxed{0.0061199}

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