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Mrrafil [7]
3 years ago
13

Please please please help me please

Mathematics
1 answer:
Step2247 [10]3 years ago
6 0

Answer:

Each term is a sum of the two previous terms like the fibonacci sequence, but the sum of the two starting terms of the lucas sequence is followed by 2 then 1, rather than 0 then 1 for the fibannaci sequence.

These are integer sequences.

The sum of the two previous terms can be represented by:

fn = fn-1 + fn-2.

These numbers can be obtained by adding the previous corresponding term of the fibonacci sequence by the next corresponding term to get the corresponding number of the lucas sequence.

Ln = { 2 if n = 0

1 if n = 1

Ln-1 + Ln-2 if n > 1

________________

Fn+1 + Fn-1 = Ln

___________________

f(0) = -1

f(1) = 2, f(2) = 1, f(3) = 3, f(4) = 4, f(5) = 7, f(6) = 11

________________________________

f(12) = 199

________

f(12) = f(11) + f(10) = (f(10) + f(9)) + (f(9) + f(8)) = .....

given f(n) = f(n-1) + f(n-2)

____________________

f(12) = f(1) + f(2) = f(2) + f(3) = f(3) + f(4) =

f(4) + f(5) = f(5) + f(6) = f(6) + f(7) =

f(7) + f(8) = f(8) + f(9) = f(9) + f(10) =

f(10) + f(11) = f(12) →

f(12) = 2 + 1 = 1 + [3] = 3 + [4] = 4 + [7] =

7 + [11] = 11 + [18] = 18 + [29] = 29 + [47] =

47 + [76] = 76 + [123] = <u>199</u>

_____________________

Explicit formula

for n is an integer.

Nth term of the lucas sequence.

As you can see, the golden ratio

( 1 + √5 / 2) appears in here.

L(n) = ((1 + √5) / 2)ⁿ⁻¹ + ((1 – √5) / 2)ⁿ⁻¹

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Answer:

40

Step-by-step explanation:

The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets .

Let n be the number of baskets and let t be the mount of time it takes to make the basket. This means that:

n α t

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She can make 4 baskets in every 1/2 hour.

This means that:

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The time is now 5 hours (t = 5). Therefore:

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She can make 40 baskets in 5 hours.

8 0
3 years ago
Steve built a square hamster pen that has a perimeter of 240 centimeters What is the length of one side of Steve’s hamster pen?
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Step-by-step explanation:

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5x(6x+28)=-23 <br><br>Help I don't understand
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Answer:

Solve the equation for  x  by finding  a,  b, and  c  of the quadratic then applying the quadratic formula.


Exact Form:


x  =  −  70  ±  √4210/30


Decimal Form:


x  =  −0.03


Step-by-step explanation:

5x(6x+28)=−23


Step 1: Simplify both sides of the equation.


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Step 2: Subtract -23 from both sides.


30x2+140x−(−23)=−23−(−23)


30x2+140x+23=0


Step 3: Use quadratic formula with a=30, b=140, c=23.


x=−b±√b2−4ac/2a


x=−(140)±√(140)2−4(30)(23)/2(30)


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