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Marianna [84]
3 years ago
8

Please i need an answer urgently. Sum of 3 terms are 252, first term is 192. Find common ratio

Mathematics
1 answer:
Viefleur [7K]3 years ago
6 0

Answer:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Step-by-step explanation:

<u>Geometric Sequences</u>

The geometric sequence is given as:

a_1, a_1r, a_1r^2, a_1r^3,..., a_1r^{n-1}

Where n is the number of the term, n≥1, and r is the common ratio.

The sum of n terms of the geometric sequence is given by:

\displaystyle S_n=a_1\frac{r^n-1}{r-1}

We are given: S3=252, a1=192, thus substuting:

\displaystyle 252=192\frac{r^3-1}{r-1}

Dividing by 12:

\displaystyle 21=16\frac{r^3-1}{r-1}

Recall that:

r^3-1=(r-1)(r^2+r+1)

Substituting:

\displaystyle 21=16\frac{(r-1)(r^2+r+1)}{r-1}

Simplifying:

21=16(r^2+r+1)=16r^2+16r+16

Rearranging:

16r^2+16r+16-21=0

16r^2+16r-5=0

Rewriting:

16r^2-4r+20r-5=0

Factoring:

4r(4r-1)+5(4r-1)=0

(4r-1)(4r+5)=0

Solving:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Both solutions are valid

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Answer 28.

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Answer 29.

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A rectangular parking area measuring 5000 ft squared is to be enclosed on three sides using​ chain-link fencing that costs ​$5.5
kaheart [24]

Answer:

Dimensions: 75.3778 ft and 66.3325 ft

Minimum price: $1658.31

Step-by-step explanation:

Let's call the length of the parking area 'x', and the width 'y'.

Then, we can write the following equations:

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x * y = 5000

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P = 11*x + 12.5*y

From the first equation, we have that y = 5000/x

Using this value in the equation for P, we have:

P = 11*x + 12.5*5000/x = 11*x + 62500/x

To find the minimum of this function, we need to take its derivative and then make it equal to zero:

dP/dx = 11 - 62500/x^2 = 0

x^2 = 65000/11

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This is the x value that gives the minimum cost.

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y = 5000/75.3778 = 66.3325

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5 0
3 years ago
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