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1 month ago

Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...

Mathematics

1 answer:

PIT_PIT [12.4K]1 month ago

5 0

Answer:

The recursive formula needed is:

$a_n=(-3)\times a_{n-1}$

Detailed explanation:

We are given a geometric sequence:

6, -18, 54, -162, ...

By examining the terms, we see this sequence is a geometric progression (G.P.) with a common ratio, r, of -3.

Let $a_n$ denote the nth term.

This implies:

$a_1=6, a_2=-18, a_3=54, a_4=-162,......$

Since the common ratio equals -3,

therefore,

$a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}$

Thus, the recursive formula for this geometric sequence is:

$a_n=(-3)\times a_{n-1}$

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Maximum value of x3y3 + 3 x*y when x+y = 8.

Inessa [12570]

Response:

The outcome is 4144.

Detailed explanation:

We need to determine the peak value of f(x)= $x^{3}y^{3}+3xy$ when $x+y=8$

We can represent $x+y=8$ as $y=8-x$

Plugging the value of y

$f(x)=x^{3}(8-x)^{3} +3x(8-x)$

= $3x^{2}(8-x)^{2}[-x+8-x]+3[-x+8-x]$

= $3(8-2x)[x^{2}(8-x)^{2}+1]$

To find the maximum, we'll set the equation to 0.

Thus, we find:

$8-2x=0$ => x = 4

And since $y=8-x$

$y =8-4= 4$ > y = 4

Hence, we will substitute these values into the equation to ascertain the maximum value.

= $x^{3}y^{3}+3xy$

= $xy(x^{2}y^{2}+3)$

= $4\times4((16\times16) +3)$

= $16(259)$ = 4144

8 0

29 days ago

Read 2 more answers

Zach uses his car for business and must keep accurate driving records so that his company will reimburse him for car expenses. W

zzz [12365]

To determine the total distance traveled, subtract the starting mileage from the ending mileage: 28017 - 26645 = 1372 miles. To find out how many gallons of gas were purchased, divide that distance by the average miles per gallon: 1372/48 = 28.583 gallons. Then, to calculate the cost per gallon, divide the total amount spent by this number: 62.28/28.583 = $2.179 per gallon of gas.

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11 days ago

Last week, the price of apples at a grocery store was $1.60 per pound. This week, apples at the same grocery store are on sale a

tester [12383]

Answer:

$6.48

Step-by-step explanation:

Initially calculate the 10% discount on $1.60, which results in $1.44. Then multiply $1.44 by 4.5 to find the total, yielding $6.48.

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1 month ago

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Which expression is equivalent to StartFraction 3 x Superscript negative 6 Baseline y Superscript negative 3 Baseline Over 15 x

zzz [12365]

Answer:

The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

Step-by-step explanation:

In order to simplify the expression $\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }$ where x ≠ 0, y ≠ 0, we must work through the given expression.

$\frac{3x^{-6}y^{-3} }{15x^{2}y^{10} }\\= \frac{3}{15} x^{-6-2}y^{-3-10}\\ = \frac{3}{15}x^{-8}y^{-13} \\ =\frac{1}{5}x^{-8}y^{-13} \\$

The appropriate expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

6 0

1 month ago

Deep Blue, a deep sea fishing company, bought a boat for $250,000. After 9 years, Deep Blue plans to sell it for a scrap value o

Leona [12618]

Answer:

Hence, utilizing linear depreciation gives us 17222.22.

Step-by-step explanation:

The boat's initial value is noted to be $250,000.

The straight-line depreciation method for calculating a boat is as follows:

Cost of the boat is $250,000.

Deep Blue anticipates selling it for $95,000 after 9 years.

Employing the formula, we calculate:

(250000-95000)/9=155000/9=17222.22

Thus, the outcome using linear depreciation is 17222.22.

8 0

1 month ago