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mamaluj [8]
3 years ago
12

Define the sequence recursively using function notation. 2.5, 7.5, 22.5, 67.5, 202.5,...

Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
5 0

Answer: Aₙ = Aₙ₋₁*3;  where A₀ = 2.5

Step-by-step explanation:

Let's try with some known sequences:

Arithmetic.

The difference between consecutive terms is constant:

7.5 - 2.5 = 5

22.5 - 7.5 = 15

We can already see that it is not an arithmetic sequence.

Geometric:

The ratio between consecutive terms is constant.

7.5/2.5 = 3

22.5/7.5 = 3

67.5/22.5 = 3

...

We can already see that this is a geometric sequence.

Then we can write the n-th term as:

Aₙ = Aₙ₋₁*3, where A₀ = 2.5

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What is 2<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D" id="TexFormula1" title="\frac{1}{5}" alt="\frac{1}{5}" align="
vivado [14]

2\dfrac{1}{5}+1\dfrac{1}{10}=2+\dfrac{1}{5}+1+\dfrac{1}{10}=(2+1)+\left(\dfrac{1}{5}+\dfrac{1}{10}\right)\\\\=3+\left(\dfrac{1\cdot2}{5\cdot2}+\dfrac{1}{10}\right)=3+\left(\dfrac{2}{10}+\dfrac{1}{10}\right)=3+\dfrac{2+1}{10}=\boxed{3\dfrac{3}{10}}

7 0
3 years ago
A game involves correctly choosing the 5 correct numbers from 1 through 18 that are randomly drawn. What is the probability that
bazaltina [42]

Answer:

=\frac{1}{8568}\ = .00011\\\ =\frac{7}{8568}  = .00081

Step-by-step explanation:

5/18\cdot \:4/17\cdot \:3/16\cdot \:2/15\cdot \:1/14=\frac{1}{8568}

4 0
3 years ago
Can someone pls help me . ASAPPP
STALIN [3.7K]

Volume without holes = 3 x 6 x 11 = 198 cubic inches.

Calculate volume of one hole:

3.14 x 0.5^2 x 3 = 2.355 cubic inches

There are 3 holes: 3 x 2.355 = 7.065

Subtract volume of the holes from the brick:

198 - 7.065 = 190.935 cubic inches.

Rounded to the nearest tenth: 190.9 cubic inches.

8 0
3 years ago
Read 2 more answers
Question 25
AysviL [449]

Answer:

120

Step-by-step explanation:

First, you have to calculate the money that Seth would spent if he goes to 30 movies if his father gets the summer movie pass by adding up the cost of the pass plus the result of multiplying the cost per movie with the pass for the number of movies:

30+(3*30)=30+90=120

Second, you need to calculate the money that Seth would spent if he goes to 30 movies without the pass by multiplying the normal price per movie for the number of movies:

8*30=240

Third, you need to find the difference between both costs:

240-120=120

According to this, the answer is that if Seth plans to go to 30 movies this summer, he would save 120.

8 0
3 years ago
Surface area of a cube or a rectangular prism
suter [353]

Answer:

96 cm^2

Step-by-step explanation:

All faces of a cube are equal in area.

Therefore the Formula for SA of a cube is 6*s^2

SA = 6*4*4 = 96

5 0
2 years ago
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