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2 years ago

Write an explicit formula for the geometric sequence below and use it to find the 9th term. 256, 64, 16, 4, . . .

Mathematics

1 answer:

Nastasia [14]2 years ago

7 0

im doing this problem right now---

ok so a1=256 a2=64 a3=15 a4=4... find a9

the sequence divides by 1/4 every term

an=a1*r^n-1

an=(256)*(1/4)^n-1

replace n with 9

A9=(256)*(1/4)^9-1

A9=(256)*(1/4)^8

=(256)*(1/4)

A9=64^8

1/256 or a9= 0.00390625

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Number of alluvial wells = 349

Number of quaternary wells = 143

Number of alluvial wells that had concentrations above 0.1 = 182

Number of quaternary wells that had concentrations above 0.1 = 112

Average of alluvial wells = 0.27

Standard deviation = 0.4

Average of quaternary wells = 1.62

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$\dfrac{\alpha}{2}=2.5\%\\\\z_{\frac{\alpha}{2}}=1.96$

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$(1.62-0.27)\pm 1.96\sqrt{\dfrac{0.4^2}{349}+\dfrac{1.7^2}{143}}\\\\=1.35\pm 1.96\times 0.020\\\\=(1.35-0.040,1.35+0.040)\\\\=(1.31,1.39)$

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