A sequence has the recursive definition of f(1)=2/3, f(n)=f(n-1)×3/2 for n≥2


Right the first five terms of the sequence

Leave answers as fractions

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]f(1)=2/3\\f(2)=f(1)\times (3/2)=(2/3)\times(3/2)=1\\f(3)=f(2)\times (3/2) = 1\times (3/2) = 3/2\\f(4)=f(3)\times (3/2) = (3/2)\times (3/2) = 9/4\\f(5)=(f(4)\times (3/2) = (9/4)\times (3/2) = 27/8[/tex]

So the first five terms are 2/3, 1, 3/2, 9/4, 27/8.

Answer 2

The first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the  f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that:

f(1)=2/3,

f(n) = f(n -1)×(3/2); for n ≥ 2

Plug n = 2

f(2) = f(2 -1)×(3/2)

f(2) = f(1)×(3/2)

f(2) = (2/3)(3/2)

f(2) = 1

Similarly;

f(3) = 3/2

f(4) = 94/

f(5) = 27/8

The first five terms are 2/3, 1, 3/2, 9/4, and 27/8.

Thus, the first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the  f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.

Learn more about the sequence here:

brainly.com/question/21961097

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Related Questions

The pretzel shop usually sell an average of 11 original pretzels and 7 cinnamon pretzels each hour. If they sold 132 original pretzels today about how many cinnamon pretzels did they probably sell?

Answers

132/11 is 12
So 7*12 is 84
They shouldve sold around 84 cinnamon pretzels

if f(x)=3x-7 evaluate f(-2w+1/2)=

Answers

Step-by-step explanation:

f(x) = 3x - 7

f (-2w + .5) = 3(-2w + .5) - 7

= -6w + 1.5 -7

= -6w - 5.5

-3(x² +2x-3)+3(x²+4x)​

Answers

6x + 9

I hope this helps!

Answer:

= 6x +9

Step-by-step explanation:

1. you need to multiply -3 by x² + 2x - 3

so you got -3x² -6x + 9

2. Then, you need to multiply 3 by (x²+4x)

= 3x² + 12x

3. -3x² - 6x + 9 + 3x² + 12x

4. then you need to solve with the same

= - 3x² + 3x²

= 0

= - 6x + 12x

= 6x

5. lastly you will got the answer.

# = 6x +9

i^32=......................

Answers

i^32 = (i^4)^8 and i^4 = 1

so (i^4)^8 =1^8 = 1

The trick on all questions like this is to get as many i^4’s out of the way, since they’re all just 1s.

driver a had a speed of 145.155 and driver b had a speed of 145.827 and driver c had a speed of 1144.809.Driver d had a speed between driver a and driver c. Write a possible speed for driver d. ​

Answers

The answer is 1075.678

Write two fractions that are equivalent to 5/20.

Answers

Answer:

[tex] \frac{5}{20} = \frac{1}{4} = \frac{10}{40} \\ thank \: you[/tex]

what is the radius of 28mm

Answers

If you are talking about radius of circle it is 2463

the quotient of five times a number 7 is no more than 10​

Answers

Answer:

[tex]x \ge3.5[/tex]

Step-by-step explanation:

First, write the given in the form of a mathematical equation rather than words. I'll call the mystery number given in the question [tex]x[/tex]:

[tex]\frac{5*7}{x} \leq 10[/tex]

Simplify:

[tex]\frac{35}{x} \leq 10[/tex]

Solve for x:

[tex]\frac{35}{x} *x\leq 10*x[/tex]

Simplify the fraction:

[tex]35\leq 10x[/tex]

Divide by 10 to isolate x:

[tex]\frac{35}{10} \leq x[/tex]

Flip the equation around to make it easier to read:

[tex]x \ge \frac{35}{10}[/tex]

Simplify the fraction:

[tex]x \ge \frac{7}{2}[/tex] or [tex]x \ge3.5[/tex]

a number w multiplied by 42

Answers

Answer:

42 = 1 x 42, 2 x 21, 3 x 14, or 6 x 7.

Jane drove 406 miles in 7 hours.
At the same rate, how long would it take her to drive 522 miles?
9 hours
Х
6
?

Answers

Answer:

9 hours

Step-by-step explanation:

Pls help I’m so confused

Answers

[tex]5x-6-x=2x+2\\\\5x-x-2x=2+6\\\\2x=8 \ \ /:2\\\\x=4\\\\\huge\boxed{\text{There is one solution at x=4}}[/tex]

Answer:

There is one solution at x+4

Step-by-step explanation:

Can someone help me.....​

Answers

Answer:

The square root of 2 is between 1 and 2, so radical 2 is about 1.4.

Step-by-step explanation:

You can plot a 1 on the very left and a 2 on the very right of the number line.

Since there is no formal square root of 2, you have to estimate.

It has to be less than 2 because if you multiply 2 * 2 you get 4 and that's too big; we want to get 2.

It also has to be greater than 1 because 1 * 1 = 1 and that's too low.

I would estimate it to be right before the middle line.

Simplify the expression:
1+4(2x-3)

Answers

Answer:

8x - 11

Step-by-step explanation:

?

just do the multiplications and add things up.

1 + 4(2x - 3) = 1 + 8x -12 = 8x - 11

1+4(2x-3)
1+8x-12
8x-11

Need help with #12
Please help

Answers

Step-by-step explanation:

If the figure is triangle then,

Let PR be x

So,

PQ+QR+PR= 180 (Sum of all the angles of the triangle)

Therefore,

6x+25+16-3x+x=180

4x+36=180

4x= 180/36

x= 144/4

X= 36

NOW,

PQ= 6x+25

= 6(36)+25

= 216+25 = 241= PQ.

QR = 16-3x

= 16-3(36)

= 16-108

= -92

PR = 36

hope it helps

Answer:

PR = 36

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

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Answers

Answer:

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Step-by-step explanation:

Which is true about the functional relationship shown in the graph?

A. The weight of the apples is a function of their cost.
B. The weight of the apples is a function of the number of apples.
C. The cost of the apples is a function of their weight.
D. The cost of the apples is a function of the type of apple​

Answers

Answer:

A. The weight of the apples is a function of their cost.

Step-by-step explanation:

In the graph it shows the more the apples weight the cost increase, therefore A is your answer.

Answer - A

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Cost being the dependent variable
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Answer:

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Answers

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The range
The mode

Answers

Answer:

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Answers

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Step-by-step explanation:

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Alyssa, Reggie and Cassie are meeting some friends at the movies and have stopped
at the refreshment stand. The table below shows some of the items for sale and their
prices.
Alyssa has $7 and would like to buy fruit snacks for as many of her friends as
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Answers

Answer:

fruit snack = $2.00. Alyssa can buy 3 fruit snacks and she will have $1 left over. hope this helps

Step-by-step explanation:

- Zombie

Answer:

Hot dog+Nachos+Fruit snack

2.50 + 2.50 + 2.00

Step-by-step explanation:

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Equation:
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Answers

Answer:

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Step-by-step explanation:

The variable is g, the amount of gigabytes she uses and each gigabyte costs $4 therefore the equation must be set as the flat fee, $50.50 plus 4g since it costs $4 per gigabyte to be less or equal to $56.10 since Aubree wants to stay below $56.10.

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Answers

Answer:

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Step-by-step explanation:

-0.58x+0.38x=4.8

Combine like terms:

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Answers

Answer:

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I hope it will help you a lot.

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Step-by-step explanation:

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