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Sagot :
We are given the following sequence:
[tex]6,18,54,162[/tex]We notice that each term is obtained by multiplying the previous by 3, as follows:
[tex]\begin{gathered} 6\times3=18 \\ 18\times3=54 \\ 54\times3=162 \end{gathered}[/tex]This is known as a geometric sequence. The iterative rule for a geometric sequence has the following form:
[tex]a_n=a_1r^{n-1}[/tex]Where:
[tex]\begin{gathered} a_1=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ the place of the term we want to }\det er\min e \end{gathered}[/tex]The common ratio is the number we have the multiply the previous term to get the next term, in this case, we have r = 3. Substituting we get:
[tex]a_n=6(3)^{n-1}[/tex]Since we can't simplify any further this is the iterative rule.
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