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8_murik_8 [283]
2 years ago
15

Write an explicit formula for the arithmetic sequence whose common difference is -18

Mathematics
2 answers:
drek231 [11]2 years ago
7 0

Let the first term be a(0).  Then the formula for a(n) is a(0)-18(n-1).

Check:  What's the first term?  Let n = 1:  a(1) = a(0)-18(1-1) = a(0) (correct)

What's the second term?    Let -n =2:  a(2) = a(0)-18(2-1) = a(0) - 18

and so on.

wolverine [178]2 years ago
4 0

Answer : The an explicit formula for the arithmetic sequence will be, a(n)=a-18\times (n-1)

Step-by-step explanation :

Arithmetic progression : It is a sequence of numbers in which the difference of any two successive number is a constant.

The general formula of arithmetic progression is:

a(n)=a+(n-1)d

where,

a(n) = nth term in the sequence

a = first term in the sequence

d = common difference

n = number of terms in the sequence

As we are given that:

Common difference = d = -18

Thus, the formula of arithmetic progression will be:

a(n)=a+(n-1)d

a(n)=a+(n-1)\times (-18)

a(n)=a-18\times (n-1)

For example:

Let n=1 :

a(n)=a-18\times (n-1)\\\\a(1)=a-18(1-1)=a

Let n=2 :

a(n)=a-18\times (n-1)\\\\a(2)=a-18(2-1)=a-18

Let n=3 :

a(n)=a-18\times (n-1)\\\\a(3)=a-18(3-1)=a-36

The sequence will be, a, (a-18), (a-36),.........

Thus, the an explicit formula for the arithmetic sequence will be, a(n)=a-18\times (n-1)

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Blababa [14]

Answer:

- \frac{9}{10}

Step-by-step explanation:

Step 1: Add the numerator fractions.

2/5 + 3/10

Here we have to find LCD, the LCD of 5 and 10 is 10

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Therefore,  2/5 + 3/10 = ---------------  = ------------------

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The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

<h3>How to find the factors of a quadratic expression?</h3>

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

b = \alpha + \beta \\ ac =\alpha \times \beta

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

4x^2 + 28x + 49

So we've to find two numbers such that:

Their sum = b =  28

Their product = ac = 4\times 49 = 196

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

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Writing b = 28 as sum of 14 twice, we get:

4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 =  2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49  = (2x+7)(2x+7)

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

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Answer:

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Step-by-step explanation:

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<u>Now, by using the following formula, we can determine the population p in any given day t:</u>

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FV(p)= 1,500*(1.16993^10)

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