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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
216
,
36
,
6
,
.
.
.
216,36,6,...
Find the 7th term.
Find the 7th

Sagot :

Semsee45idn

Answer:

[tex]\dfrac{1}{216}[/tex] = 0.005 (nearest thousandth)

Step-by-step explanation:

geometric series formula:  [tex]a_n=ar^{n-1}[/tex]

where a is the first term and r is the common ratio

Given:

  • [tex]a_1=216[/tex]
  • [tex]a_2=36[/tex]
  • [tex]a_3=6[/tex]

[tex]r=\dfrac{a_2}{a_1}=\dfrac{36}{216}=\dfrac16[/tex]

[tex]\implies a_n=216 \cdot \dfrac16^{n-1}[/tex]

[tex]\implies a_7=216 \cdot \dfrac16^{7-1}=\dfrac{1}{216}=0.005[/tex]

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