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Sagot :
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]
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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