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# 2: 200, 100, 50, 25 ... geometrik dizisi göz önüne alındığında (Bu biraz zor)
Açık formülü yazın.
• Dizinin 15. terimini belirleyin?
Açık formülü yazın.
• Dizinin 15. terimini belirleyin?
Answer:
see explanation
Step-by-step explanation:
The explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 200 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{100}{200}[/tex] = [tex]\frac{1}{2}[/tex] , then
[tex]a_{n}[/tex] = 200 [tex](\frac{1}{2}) ^{n-1}[/tex] ← explicit formula
The 15 th term is then
a₁₅ = 200 × [tex](\frac{1}{2}) ^{14}[/tex]
= 200 × [tex]\frac{1}{16384}[/tex]
= [tex]\frac{200}{16384}[/tex] ← divide numerator/ denominator by 8
= [tex]\frac{25}{2048}[/tex]
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