The rule of Fibonacci Sequence is F ( n ) = F ( n - 2 ) + F ( n - 1 ) . Find the 11 th to 20 th Fibonacci numbers.

Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , and so on. Let us tabulate the Fibonacci sequence: Fibonacci series is given by F n = F n - 2 + F n - 1 ∴ F ( 11 ) = F ( 11 - 2 ) + F ( 11 - 1 ) = F ( 9 ) + F ( 10 ) Similarly F ( 12 ) ; = F ( 12 - 2 ) + F ( 12 - 1 ) = F ( 11 ) + F ( 10 ) F ( 13 ) = F ( 12 ) + F ( 11 ) F ( 14 ) = F ( 13 ) + F ( 12 ) … … F ( 20 ) = F ( 19 ) + F ( 18 ) The Fibonacci series given by

MEDIUM

Earn 100

In the given graph sheet draw and colour how the Fibonacci number pattern makes a spiral in the Golden Rectangle.

Important Questions on Sequences and Sets

HARD

Mathematics>Algebra>Sequences and Sets>Sequences

Let

A_{1}, A_{2}, A_{3}, \dots . .

be squares such that for each

n ⩾ 1,

the length of the side of

A_{n}

equals the length of diagonal of

A_{n + 1}

. If the length of

A_{1}

12 cm

, then the smallest value of

n

for which area of

A_{n}

is less than one, is

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Mathematics>Algebra>Sequences and Sets>Sequences

The sum

1 + \frac{1^{3} + 2^{3}}{1 + 2} + \frac{1^{3} + 2^{3} + 3^{3}}{1 + 2 + 3} + . . . + \frac{1^{3} + 2^{3} + 3^{3} + . . . + 15^{3}}{1 + 2 + 3 + . . . + 15} - \frac{1}{2} (1 + 2 + 3 + . . . + 15)

is equal to

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Mathematics>Algebra>Sequences and Sets>Sequences

The sum of the following series

1 + 6 + \frac{9 (1^{2} + 2^{2} + 3^{2})}{7} + \frac{12 (1^{2} + 2^{2} + 3^{2} + 4^{2})}{9} + \frac{15 (1^{2} + 2^{2} + \dots + 5^{2})}{11} + . . . .

up to

15

terms, is:

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Mathematics>Algebra>Sequences and Sets>Sequences

1 + \frac{1 + 2}{2!} + \frac{1 + 2 + 3}{3!} + \frac{1 + 2 + 3 + 4}{4!} + \dots \infty =

HARD

Mathematics>Algebra>Sequences and Sets>Sequences

Let

n_{1}, n_{2}, n_{3}

... be the increasing sequence of smallest natural numbers each of which leaves remainder

r

when it is divided by

(r + 1)

for

r = 1, 2, 3, \dots 8

. When

n_{2008}

is divided by

11,

the remainder is -

MEDIUM

Mathematics>Algebra>Sequences and Sets>Sequences

Choose the missing number of the given fibonacci series that has to come before $34$ .

$0, 1, 1, 2, 3, 5, 8, 13, 34$

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

The difference between

6^{t h}

term and

5^{t h}

term in the fibonacci sequence is

MEDIUM

Mathematics>Algebra>Sequences and Sets>Sequences

The value of

Σ_{r = 1}^{n} \frac{1}{\sqrt{a + rx} + \sqrt{a + (r - 1) x}}

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Mathematics>Algebra>Sequences and Sets>Sequences

The difference between the

18 t h

and

17 t h

Fibonacci number is

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Mathematics>Algebra>Sequences and Sets>Sequences

Define the Fibonacci numbers. Calculate the value of the

12^{th}

and the

13^{th}

Fibonacci numbers. The

9^{th}

and

10^{th}

terms in the sequence are

21

and

34

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Given that one pair of new born rabbits they produce a new pair each month and from the second month, each new pair can breed themselves. Find how many pairs of rabbits are bred from one pair in a year, and find the relationship between the number of months and the number of pairs of rabbits by tabulation (a pair means (a male and a female)).

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Mathematics>Algebra>Sequences and Sets>Sequences