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vazorg [7]
3 years ago
14

Given the geometric sequence with the first three terms shown as (2,10,50..) answer the following questions:

Mathematics
1 answer:
natta225 [31]3 years ago
8 0
The recursive definition of the sequence is :

\bf a_n = 2(5)^{n-1}


The 10th term is:

a_{10} = 2(5)^{10-1}

a_{10} = 2(5)^9

\bf a_{10} = 3906250

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Julia rides her horse 18 km with a constant speed of 6km/hr and another 24 km with a constant speed of 12 km/hr. What is her ave
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Answer:

8.4 km/hr.

Step-by-step explanation:

We have been given that Julia rides her horse 18 km with a constant speed of 6 km/hr.

Let us find the time taken by Julia to cover a distance of 18 km.

\text{Time}=\frac{\text{Distance}}{\text{Speed}}

\text{Time taken to cover 18 km}=\frac{18\text{ km}}{\frac{6\text{km}}{\text{hour}}}

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\text{Time taken to cover 18 km}=\frac{18}{6}\times\text{hour}

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We are also told that she rides another 24 km with a constant speed of 12 km/hr.

Let us find the time taken by Julia to cover a distance of 24 km.

\text{Time taken to cover 24 km}=\frac{24\text{ km}}{\frac{12\text{km}}{\text{hour}}}

\text{Time taken to cover 24 km}=\frac{24\text{ km}}{12}\times\frac{\text{hour}}{\text{km}}

\text{Time taken to cover 24 km}=\frac{24}{12}\times\text{hour}

\text{Time taken to cover 24 km}=2\text{ hour}

Since we know that \text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}.

Upon substituting our values in above formula we will get,

\text{Julia's average speed}=\frac{18\text{ km}+24\text{ km}+}{3\text{ hour}+2\text{ hour}}

\text{Julia's average speed}=\frac{42\text{ km}}{5\text{ hour}}

\text{Julia's average speed}=\frac{8.4\text{ km}}{\text{ hour}}

Therefore, Julia's average speed is 8.4 km per hour.


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