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3 years ago

What is the recursiveformula for this geometric sequence? 4,-12,36,108

Mathematics

1 answer:

Vlad1618 [11]3 years ago

8 0

Answer:

a[1] = 4

a[n] = -3·a[n-1]

Step-by-step explanation:

The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.

If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...

a[1] = 4 . . . . . . . . . . . first term is 4

a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one

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I need help! Will mark Brainliest for full answer!!!

Softa [21]

Answer:

Part a .............> x = 11

Part b .............> k = 57.2

Part c .............> y = 9.2

Explanation:

The three problems deal with inverse variation between two variables

An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)

Mathematically, an inverse variation relation is represented as follows:

$y = \frac{k}{x}$

where x and y are the two variables and k is the constant of variation

Now, let's check the givens:

Part a:

We are given that y = 3 and k = 33

Substitute in the original relation and solve for x as follows:

$y = \frac{k}{x}\\ \\3 = \frac{33}{x}\\ \\x=\frac{33}{3}=11$

Part b:

We are given that y = 11 and x = 5.2

Substitute in the original relation and solve for k as follows:

$y=\frac{k}{x}\\ \\11=\frac{k}{5.2}\\ \\k=11*5.2=57.2$

Part c:

We are given that x=7.8 and k=72

Substitute in the original relation and solve for y as follows:

$y=\frac{k}{x}=\frac{72}{7.8}=9.2$ to the nearest tenth

Hope this helps :)

6 0

2 years ago

Samantha is taking out a loan for $17,452 at 6% simple interest for one year. How much interest will she pay?

andrew11 [14]

Answer:

She will pay $1,047.12 interest for one year

Step-by-step explanation:

Simple Interest

Occurs when interest is calculated on the original principal only.

Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.

The interest earned is calculated as follows:

I=P.r.t

Where:

I = Interest

P = initial principal balance or loan

r = interest rate

t = time

Samantha takes out a loan for $17,452 at r=6%=0.06 simple interest for t=1 year. Calculating the interest:

$I=\$17,452*0.06 *1$

I = $1,047.12

She will pay $1,047.12 interest for one year

6 0

3 years ago

776 kilometers in 56 hours = 679 kilometers in

storchak [24]

The answer is 49 hours

4 0

3 years ago

Mary spent a total of $322.78 for a party. She spent $200.66 on food, plus an additional $30.53 for each hour of the party. How

bulgar [2K]

Let h equal the length of the party in hours

200.66 + 30.53h = 322.78

now just solve for h :)
30.53h = 122.12
h = 4

so the party was 4 hours long

8 0

2 years ago

Read 2 more answers

a cruise ship heads due west from a port 3 miles directly south of San Francisco. If the ship is travelling at a constant rate o

Anton [14]

Answer:

16.7

Step-by-step explanation:

speed is constant at 17 mph

Distance covered after one hour = 17 miles

Distance between port and San Francisco = 3 miles

Speed at which distance changes 1 hour after leaving port :

r² = 17² - 3²

r² = 289 - 9

r = √280

r = 16.733

= 16.7 (nearest tenth )

3 0

3 years ago