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elena-s [515]
1 year ago
9

The bids in an online auction are represented by the arithmetic sequence shown below. Write an explicit formula to represent the

bids as an arithmetic sequence. What is the twelfth bid?
195, 205, 215, 225,...
A(n) =
A(12) =
(Type an expression using n for the variable.)
(Simplify your answer.)

Mathematics
1 answer:
zmey [24]1 year ago
8 0

(a) The nth term of the sequence is given by A(n)=195 + (n - 1)10.

(b) The 12th term of the sequence is A(12) = 305.

<h3>What is an arithmetic sequence?</h3>

One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression.

A mathematical sequence has the following structure: a, a+d, a+2d, a+3d, etc., up to n terms. The initial term is a, the shared distinction is d, and n is the total number of words. Find the AP, the first term, the number of terms, and the common difference for the computation using the arithmetic sequence formulae. To determine the nth term, sum, or common difference of a given arithmetic sequence, many formulae related to arithmetic series are utilized.

A(n)=195+(n-1)10

The given arithmetic sequence is 195, 205, 215, 225,.....

The first term a =195

The common difference d= 205-195

d =215-205

d =225-215

So, d = 10

(a) The nth term is given by

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

A(n)=195+(n-1)10

(b) For n=12, the 12th term is given by

A(12)=195+11(10)

A(12)=305

Therefore, A(n)=195+(n-1)10

And A(12)=305

To know more about the arithmetic sequences, visit:

brainly.com/question/15412619

#SPJ1

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Charlie runs a book rental business. He currently charges $3 per book and rents out an average of 38 books a day.
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Answer:

b(x) = (3+0.5x) (38-4x)

Step-by-step explanation:

Let the generated revenue per day be b(x)

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Formula to be used to generate the revenue generated is expressed using the formula:

b(x) = Price × Quantity

Next is to derive the price and quantity function in terms of x.

For the price:

If he currently charges $3 per book

Let derive the price function for the model and x number of price increase for every 50 cents, then

Price = ($0.5 of x)+$3

Price = $3+$0.5x

Price = $(3+0.5x)

For the quantity:

Number of books rent out per day = 38

If for every 50cents increase in rental price x, the average business can expect to lose 4 rentals a day, then the total lost per quantity = 4x

Quantity per time = Number of books rent out daily - loss on each book

Quantity = $(38-4x)

Next is to substitute the price and quantity function into the revenue formula above:

Revenue = Price × Quantity

Revenue = (3+0.5x)(38-4x)

Hence the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50 price increases is b(x) = (3+0.5x)(38-4x)

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