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3 years ago

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170.

Mathematics

1 answer:

Illusion [34]3 years ago

5 0

Answer: the first term of the series is 128

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = a(1 - r^n)/(1 - r)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1/4 = 0.25

n = 4

S4 = 170

Therefore, the expression for the sum of the 4 terms, S4 is

170 = a(1 - 0.25^4)/(1 - 0.25)

170 = a(1 - 0.00390625)/(1 - 0.25)

170 = a(0.99609375)/(0.75)

170 = 1.328125a

a = 170/1.328125

a = 128

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For what values of the variables are the following expressions defined? 1. 5y+2 2. 18/y 3. 1/x+7 4. 2b/10−b Example: X>7

Serga [27]

Answer:

1. All real numbers

2. All real numbers except y = 0

3. All real numbers except x = -7

4. All real numbers except b = 10

Step-by-step explanation:

For any function to be defined at a particular value, it should not be approaching to a value $\infty$ or it should not give us the $\frac{0}{0}$ (zero by zero) form when the input is given to the function.

The value of function will depend on the denominator.

Now, let us consider the given functions one by one:

1. 5y+2

Here denominator is 1. So, it can not attain a value $\infty$ or $\frac{0}{0}$ (zero by zero) form

So, for all real numbers, the function is defined.

$2.\ \dfrac{18}{y}$

At y = 0, the value

$At\ y =0, \dfrac{18}{y} \rightarrow \infty$

So, the given function is defined for all real numbers except y = 0

$3.\ \dfrac{1}{x+7}$

Let us consider denominator:

x + 7 can be zero at a value x = -7

$At\ x =-7, \dfrac{1}{x+7} \rightarrow \infty$

So, the given function is defined for all real numbers except x = -7

$4.\ \dfrac{2b}{10-b}$

Let us consider denominator:

10-b can be zero at a value b = 10

$At\ b =10, \dfrac{2b}{10-b} \rightarrow \infty$

So, the given function is defined for all real numbers except b = 10

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Taya2010 [7]

Answer:

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Step-by-step explanation:

A length of a pen is around three inches and is reasonable but all of the others are way too big and can be measured in feet or miles.

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3 years ago

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Len [333]

Answer: 6 and 1/4

Step-by-step explanation: To solve this problem, we first leave 5/2 alone so don't do anything to it.

For our second fraction, we want to switch the numerator and the

denominator which means find the reciprocal of it.

The reciprocal of 2/5 is just the opposite of it when

you flip it and it's going to be 5/2.

Because we did the opposite there, we need to do the opposite

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So now we have 5/2 × 5/2 which is 25/4 or 6 and 1/4.

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3 years ago

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vekshin1

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3 years ago