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The term rule for the sequence $1, 1, 2, 3, 5, 8, 13, 21, . . .$

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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

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Consider the numbers between $100$ and $300$ which leaves remainder $2$ on division by $3$ .

Which is the last number in this sequence?

MEDIUM

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

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Consider the numbers between $100$ and $300$ which leaves remainder $2$ on division by $3$ .

Which is the first number in this sequence?

MEDIUM

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:

MEDIUM

Mathematics>Algebra>Sequences and Sets>Sequences

The value of

\sqrt{7 + \sqrt{7 - \sqrt{7 + \sqrt{7 - \dots \infty}}}}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Find the first four terms of the sequence defined by

a_{1} = 3

and,

a_{n} = 3 a_{n - 1} + 2

, for all

n > 1

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms of the sequence whose

n^{t h}

term is

a_{n} = {(- 1)}^{n - 1} 5^{n + 1}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

A sequence is defined by

a_{n} = n^{3} - 6 n^{2} + 11 n - 6

n \in N

. Show that the first three terms of the sequence are zero and all other terms are positive.

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms in each of the following sequence.

$a_{1} = 1 = a_{2}, a_{n} = a_{n - 1} + a_{n - 2}, n > 2$ .

HARD

Mathematics>Algebra>Sequences and Sets>Sequences

In the sequence

1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, . . .,

where

n

consecutive terms have the value

n

, the

1025^{t h}

term is

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

6 q + 1, 6 q + 4 a n d 6 q + 5 a r e : -

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms of the sequence whose

n^{t h}

term is

a_{n} = n \frac{n^{2} + 5}{4}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

The Fibonacci sequence is defined by

a_{1} = 1 = a_{2}, a_{n} = a_{n - 1} + a_{n - 2}

for

n > 2

. Find

\frac{a_{n} + 1}{a_{n}}

, for

n = 1, 2, 3, 4, 5 .

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Find the terms

a_{17} and a_{24}

in the sequence whose

n^{t h}

term is

a_{n} = 4 n - 3

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms in each of the following sequence:

a_{1} = 1, a_{n} = a_{n - 1} + 2, n > 1

HARD

Mathematics>Algebra>Sequences and Sets>Sequences

Let

a_{n}

denote the number of all

n

digit positive integers formed by the digits

0, 1

or both such that no consecutive digits in them are

0 .

Let

b_{n} =

the number of such

n

digit integers ending with digit

1

and

c_{n} =

the number of such

n

digit integers ending with digit

0 .

The value of

b_{6}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms of the sequence whose

n^{t h}

term is

a_{n} = \frac{2 n - 3}{6}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Write the first five terms of the sequence whose

n^{t h}

term is

a_{n} = \frac{n}{n + 1}

EASY

Mathematics>Algebra>Sequences and Sets>Sequences

Find the term

a_{9}

in the sequence whose

n^{t h}

term is

a_{n} = {(- 1)}^{n - 1} n^{3}

The term rule for the sequence 1,1,2,3,5,8,13,21,...

Important Questions on Sequences and Sets

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The term rule for the sequence $1, 1, 2, 3, 5, 8, 13, 21, . . .$