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xojade
27.08.2021 •
Mathematics
Find the probability that the faces do not intersect round decimal answers to the nearest percent
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Ответ:
The formula for nth term is given as![a_n = (265.625)(0.8)^{(n-1)}](/tpl/images/0366/5693/8dbd9.png)
Step-by-step explanation:
Here, 3rd term in the geometric sequence = 170
The 5th term in the sequence = 108.8
Let the first term in the sequence = a
Let the common ratio of the sequence = r
Now by the Geometric Sequence:
⇒ From above general term:
⇒![170 = a r^{2} ,\\ 108.8 = ar^{4}](/tpl/images/0366/5693/fc94e.png)
Dividing both the the equations, we get:
or,![r^{2} = \frac{1}{1.5625} = 0.64\\ \implies r = 0.8](/tpl/images/0366/5693/8db8d.png)
Hence, the common ratio r = 0.8
Now,![170 = a r^2 \implies 170 = a (0.64)\\\implies a = \frac{170}{0.64} = 265.625](/tpl/images/0366/5693/2b409.png)
⇒ a = 265.625, r = 0.8
So, the formula for nth term is given as![a_n = (265.625)(0.8)^{(n-1)}](/tpl/images/0366/5693/8dbd9.png)