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Doykar8apuzieMarian Doykar8apuzieMarian
  • 10-01-2017
  • Mathematics
Answered

Complete the pattern 486,162,54,18

Verified Answer :

LammettHash
LammettHash LammettHash
  • 10-01-2017

Each successive number is divided by 3.

\(\dfrac{486}3=162\)
\(\dfrac{162}3=54\)
\(\dfrac{54}3=18\)

and so on. The next number in the sequence is \(\dfrac{18}3=6\), and in general, you have a geometric sequence defined recursively by

\(\begin{cases}a_1=486\\\\a_n=\dfrac13a_{n-1}&\text{for }n>1\end{cases}\)

and a closed form

\(a_n=\dfrac13a_{n-1}=\left(\dfrac13\right)^2a_{n-2}=\cdots=\left(\dfrac13\right)^{n-1}a_1=\dfrac{486}{3^{n-1}}\)

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