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3 years ago

What is the value of the fourth term in the geometric sequence

Mathematics

1 answer:

ivanzaharov [21]3 years ago

6 0

Answer:

a(4) = 15/4

Step-by-step explanation:

Here we're told that the first term is a(1) = 30 and that the common factor r = 1/2.

Thus, the geometric sequence formula specific to this case is

a(n) = 30(1/:2)^(n-1).

What is the fourth term? Let n = 4,

a(4) = 30(1/2)^(4-1), or a(4) = 30(1/2)^(3), or a(4) = 30(1/8) = 30/8, or, in reduced form,

a(4) = 15/4.

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Letang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $280,00

Vanyuwa [196]

We have to calculate the EAC for both the conveyor belt system.

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Equivalent Annual Cost or (EAC) for the SYSTEM-A

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times$ tax rate )

$=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$

$= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$

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Year Annual Cost flow Present value factor Present Value of Annual

at 10% cash flow

1 -49,350 0.909091 -44,863.64

2 -49,350 0.826446 -40,785.12

3 -49,350 0.751315 -37,077.39

4 -49,350 0.683013 -33,706.71

Total $ 3.169865 $ -156,432.86

Therefore, Net Present value = present value of the annual cash flow - initial investment.

= 156,432.86 - 280,000

= $ 436,432.86 (negative)

Now the EAC or the Equivalent Annual Cost for System A :

$\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$

$=\frac{436,432.86}{3.169865}$

$= 137,681.86$ dollar (negative)

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times$ tax rate)

$=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$

$=(-78,000 \times 0.77)+(60,000 \times 0.23)$

= -$ 47,030

Year Annual Cost flow Present value factor Present Value of Annual

at 10% cash flow

1 -47,030 0.909091 -42,754.55

2 -47,030 0.826446 -38,867.77

3 -47,030 0.751315 -35,334.34

4 -47,030 0.683013 -32,122.12

5 -47,030 0.620921 -29,201.93

6 -47,030 0.564474 -26,547.21

Total $ 4.355261 $ -204,827.91

Net Present Value = Present Value of annual cash inflows – Initial Investment

$= 204,827.91 - 360,000$

= -$ 564,827.91 (negative)

EAC for system B:

Equivalent Annual Cost for system B $=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$

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7 0

3 years ago

Which of the following shows one way to simplify 43Σn=1(3+9n)?

kramer

Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

<h3>How to determine the summation expression?</h3>

The expression is given as:

43Σn=1(3+9n)

As a general rule, if a summation notation is represented using the following expression

Σ(a + bn)

The equivalent expression of the above summation notation is

Σa + bn

Where the variable a is a constant in the expression

This means that:

Σ(a + bn) = Σa + bn

Using the above equation as a guide, we have the following equivalent equation

43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n

Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

Read more about summation notation at:

brainly.com/question/16599038

#SPJ1

6 0

1 year ago