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Jia is skipping a rock across a pond. The sequence {4.2, 3.57, 3.0345, 2.5793, …} describes the height of the rock on each successive skip. Which explicit formula describes this geometric sequence?

Sagot :

semsee45

Answer:

[tex]u_n=4.2(0.85)^{n-1}[/tex]

Step-by-step explanation:

[tex]u_1=4.2\\u_2=3.57\\u_3=3.0345\\u_4=2.5793[/tex]

Geometric formula sequence:   [tex]u_n=ar^{(n-1)}[/tex]

(where [tex]a[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio)

To find the common ratio, divide one of the terms by the previous term:

[tex]r=\frac{u_2}{u_1} =\frac{3.57}{4.2} =0.85[/tex]

From inspection, [tex]a=4.2[/tex]

Therefore, [tex]u_n=4.2(0.85)^{n-1}[/tex]

brainsoft

Answer:

Answer:

[tex]{ \boxed{\tt {a _{n} = 4.94\times 0.85{}^{n} }}}[/tex]

Step-by-step explanation:

» General explicit formula for geometric sequence:

[tex]{ \tt{a _{n} = ar {}^{n - 1} }} \\ [/tex]

  • a → first term
  • a_n → nth term
  • r → common ratio

» In the sequence given;

  • n → 4
  • a_1 → 4.2
  • r → 4.2/3.57 → 17/20

[tex]{ \tt{a _{n} = 4.2 \times {( \frac{17}{20}) }^{n- 1} }} \\ \\ { \tt{{a _{n} = 4.2 \times ( \frac{17}{20}) {}^{n} \times ( \frac{17}{20}) {}^{ - 1} }}} \\ \\ { \tt{a _{n} = 4.2 \times ( \frac{17}{20}) {}^{n} \times \frac{20}{17} }} \\ \\{ \tt {a _{n} = 4.94\times 17/20 {}^{n} }}[/tex]

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