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GenaCL600 [577]
3 years ago
13

Write an equation for the nth term of the arithmetic sequence. Then find a40.

Mathematics
1 answer:
Olegator [25]3 years ago
8 0

Answer:

The nth term is: a_n = \frac{1}{4} + \frac{1}{4}(n-1)

a40 = 10

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The nth term of a sequence is given by:

a_n = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

1/4,1/2

This means that:

d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}

1/4

This means that a_1 = \frac{1}{4}

The nth term is:

a_n = a_1 + (n-1)d

a_n = \frac{1}{4} + \frac{1}{4}(n-1)

Then find a40.

a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10

So

a40 = 10

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Step-by-step explanation:

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3 years ago
What is the cost if a $1,200 washing machine after a discount if 1/5 the original price
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20 points!!
ANEK [815]

See below for the proof of the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

<h3>How to prove the equation?</h3>

The equation is given as:

\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

Take the LCM

\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)

Expand

\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)

Evaluate the like terms

\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)

Rewrite as:

\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)

Factorize the numerator

\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b) has been proved

Read more about equations at:

brainly.com/question/2972832

#SPJ1

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Answer:

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Step-by-step explanation:

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34% is the correct answer
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