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Number Theory Level 2

Find the missing term-

1, 2 , 0.5 , 4 , 0.125 , ?

40 8 32 28 20 36 16 24

Vatsalya Tandon by Vatsalya Tandon , 21, India

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2 solutions

Chew-Seong Cheong
Jan 21, 2015

Yes, it is a "Division" Fibonacci series.

a 1 = 1 , a 2 = 2 , a n = a n − 2 a n − 1 a_1 = 1, a_2 = 2, a_n = \dfrac {a_{n-2}}{a_{n-1}} for n > 2 ⇒ a 5 = a 3 a 4 = 4 0.125 = 32 n > 2\quad \Rightarrow a_5 = \dfrac {a_3}{a_4} = \dfrac {4}{0.125} = \boxed{32}

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Vatsalya Tandon
Jan 21, 2015

An n n term can be calcuated by- ( n t h − 2 ) 2 ( n t h − 1 ) 2 \sqrt{\frac{(nth-2)^{2}}{(nth-1)^{2}}}

Note: Not valid for First and Second Elements!

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