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Kaylis [27]
3 years ago
15

What is the sum of the first five terms of the geometric sequence in which a1=10 and r=1/2?

Mathematics
2 answers:
Tomtit [17]3 years ago
5 0
(10(1-(1/2)^5)/1-(1/2) = 

20(1-1/32)
=155/8
KatRina [158]3 years ago
4 0

Answer:

The sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is  \frac{1}{2} is 19\frac{3}{8}

Step-by-step explanation:

A geometric sequence is a sequence  where each term is find  by multiplying the previous term by a constant non-zero number known as the common ratio.

Here, given a_1=10 and r=\frac{1}{2}

We have to find the sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is  \frac{1}{2}.

Sum of a geometric sequence is given as :

S_n=\frac{a_1(1-r^n)}{1-r}

Substitute the values,

S_n=\frac{10(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}

Solving , we get

\Rightarrow S_n=\frac{10(1-(\frac{1}{2})^5)}{\frac{1}{2}}

\Rightarrow S_n=\frac{10(1-\frac{1}{32})}{\frac{1}{2}}      

\Rightarrow S_n=\frac{10(\frac{32-1}{32})}{\frac{1}{2}}    

\Rightarrow S_n=\frac{10(\frac{32-1}{32})}{\frac{1}{2}}  

\Rightarrow S_n=20(\frac{31}{32})  

\Rightarrow S_n=10(\frac{31}{16})  

\Rightarrow S_n=\frac{310}{16}=\frac{155}{8}  

\Rightarrow S_n=19\frac{3}{8}  

Thus, the sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is  \frac{1}{2} is 19\frac{3}{8}  

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Step-by-step explanation:

John's percentage:

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36/12= 3 and 48/12=4 therefore

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we know Don has 84 shirts so we say

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Hope that helped! Anymore questions just ask! :)

3 0
2 years ago
Select the correct location in the expression.
kogti [31]

Answer:

78

Correct term:60

Step-by-step explanation:

We are given that

\frac{4x^4-6x^3+6x+3}{x-3}

The quotient of this expression is given by

4x^3+6x^2+18x+78+\frac{183}{x-3}

We have to find the term in this expression  which contains an error.

\frac{4x^4-6x^3+6x+3}{x-3}

The quotient of this expression is given by

=4x^3+6x^2+18x+60

Dividend=Divisor\times quotient+ remainder

Using the formula

4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}

We can see that in the given expression there is 60 in place of 78.

The error in the expression of quotient is 78.

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4 0
3 years ago
A train leaves thorn junction at 1:25 p.m. and arrives in niles at 3:05 p.m. the train makes two stops along the route for a tot
KonstantinChe [14]

The time taken by the first and the second train is 1 hour 40 minutes and 1 hour 25 minutes. Then the time when the second train at Niles junction is 5:55 p.m.

<h3>What is speed?</h3>

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

\rm Speed = \dfrac{Distance}{Time}

A train leaves Thorn junction at 1:25 p.m. and arrives in Niles at 3:05 p.m. the train makes two stops along the route for a total of 15 minutes.

A second train leaves Thorn junction at 4:30 p.m. and heads to Niles.

This train does not make any stops.

Let the speed of both trains be equal.

Then the time taken by the first train will be

t₁ = 3:05 p.m. - 1:25 p.m.

t₁ = 1 hour 40 minutes

Then the time taken by the second train will be

t₂ = 1:40 - 00:15

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The time when the second train is at Niles junction will be

→ 4:30 p.m. + 1:25

→ 5:55 p.m.

More about the speed link is given below.

brainly.com/question/7359669

#SPJ1

3 0
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