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Wittaler [7]
2 years ago
8

The Fibonacci sequence is defined by $F_1 = F_2 = 1$ and $F_{n + 2} = F_{n + 1} + F_n$. Find the remainder when $F_{1999}$ is di

vided by 5.
Mathematics
1 answer:
zavuch27 [327]2 years ago
6 0

Answer:

The remainder is 1

Step-by-step explanation:

Given the Fibonacci sequence

F_1 = F_2 = 1, and

F_(n + 2) = F_(n + 1) + F_n

We want to find the remainder when F_(1999) is divided by 5.

Let us write the first 20 numbers of the sequence in (mod 5). They are

F_1 = 1,

F_2 = 1,

F_3 = 2,

F_4 = 3,

F_5 = 5 = 0 (mod 5),

F_6 = 3,

F_7 = 3,

F_8 = 1

F_(9) = 4

F_(10) = 0

F_(11) = 4

F_(12) = 4

F_(13) = 3

F_(14) = 2

F_(15) = 0

F_(16) = 2

F_(17) = 2

F_(18) = 4

F_(19) = 1

F_(20) = 0

We have: 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0

Now, 1999 = 19(mod 20)

The 19th number in the sequence is 1.

So, the remainder is 1.

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6 0
2 years ago
I rent a gym for $150 for 30 students another time I rent the gym for $270 for 70 students I need to find a fixed rate
kirza4 [7]

Answer:

Fixed rate is $60.

Step-by-step explanation:

Let us consider per student charge be 'x'.

Let us consider fixed rate be 'b'

Given:

I rent a gym for $150 for 30 students.

So we can say that;

Total amount is equal to sum of number of students multiplied by per student charge and fixed rate.

framing in equation form we get;

30x+b=150 \ \ \ \ equation \ 1

Also Given:

another time I rent the gym for $270 for 70 students.

So we can say that;

Total amount is equal to sum of number of students multiplied by per student charge and fixed rate.

framing in equation form we get;

70x+b=270 \ \ \ \ equation \ 2

Now we will subtract equation 1 from equation 2 we get;

70x+b-(30x+b)=270-150\\\\70x+b-30x-b=120\\\\40x=120

Dividing both side by 40 we get;

\frac{40x}{40}=\frac{120}{40}\\\\x=\$3

Now we will substitute the value of x in equation 1 we get;

30x+b=150\\\\30\times3+b=150\\\\90+b=150\\\\b=150-90 =\$60

So we can say that the equation can be written as;

y =3x+60

Hence we can say that fixed rate is $60 and per student charge is $3.

3 0
3 years ago
Read 2 more answers
Challenge
Katen [24]

Answer:

a). Distance from the surface of miner elevator=532 feet, Distance from the surface of equipment elevator=60 feet

b). The miner elevator is deeper since it is 472 feet deeper than the equipment elevator

Step-by-step explanation:

Equipment elevator speed=4 feet per second

Miner elevator=14 feet per second

Total time of miner elevator=(23+15)=38 seconds

Total time of equipment elevator=15 seconds

a). Distance from the surface of each elevator

Distance from the surface of miner elevator=Miner Speed×Miner Time

Distance=(14×38)=532 feet

Distance from the surface of equipment elevator=Equipment Speed×Equipment Time

Distance=(15×4)=60 feet

b). Which elevator is deeper

Distance from the surface of miner elevator=532 feet

Distance from the surface of equipment elevator= 60 feet

Difference=(532-60)=472 feet

The miner elevator is deeper since it is 472 feet deeper than the equipment elevator

5 0
3 years ago
PLEASR HELP ASAP!!!!!!! i’ll mark brainlest
Molodets [167]
This should help ^-^

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2 years ago
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The perimeter of a rhombus is 28 centimeters. What is the length of each side of the rhombus?
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