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How many three-digit numbers are divisible by $6$ in all?

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Important Questions on Sequence and Series

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Mathematics>Algebra>Sequence and Series>Arithmetic Progression

If the sum and product of the first three terms in an

A . P .

are

33

and

1155

, respectively, then a value of its

11^{t h}

term is:

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Mathematics>Algebra>Sequence and Series>Arithmetic Progression

The sum of all two digit positive numbers which when divided by

7

yield

2

5

as remainder is

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Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Three positive numbers form an increasing

G . P .

If the middle term in this

G . P .

is doubled, the new numbers are in

A . P .

Then the common ratio of the

G . P .

is :

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

x, y, z

are positive numbers in

A . P .

and

\tan^{- 1} x

\tan^{- 1} y

and

\tan^{- 1} z

are also in

A . P .

, then which of the following is correct.

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

What is the value of

21 + 22 + . . . . . . + 46

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Let

X

be the set consisting of the first

2018

terms of the arithmetic progression

1,6, 11, \dots,

and

Y

be the set consisting of the first

2018

terms of the arithmetic progression

9,16,23, \dots

. Then, the number of elements in the set

X \cup Y

is___.

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

^{n} C_{4},^{n} C_{5}

and

^{n} C_{6}

are in A.P., then

n

can be

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is

170

. If there are at least

6

houses in that row and

a

is the number of the sixth house, then

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

The difference between two numbers is

48

and the difference between their arithmetic mean and their geometric mean is

18

. Then, the greater of two numbers is

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

How many numbers are there from $200$ to $800$ which are neither divisible by $5$ nor by $7$ ?

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Let the sum of the first three terms of an A.P. be

39

and the sum of its last four terms be

178

. If the first term of this A.P. is

10,

then the median of the A.P. is :

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

What will be the

10 t h

number in the series

12, 19, 26, 33,_____?

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Let

\frac{1}{x_{1}}, \frac{1}{x_{2}}, \dots, \frac{1}{x_{n}} (x_{i} \neq 0

for

i = 1, 2, \dots ., n)

be in A.P. such that

x_{1} = 4

and

x_{21} = 20

.

n

is the least positive integer for which

x_{n} > 50

, then

\sum_{i = 1}^{n} (\frac{1}{x_{i}})

is equal to

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

a, b, c

are in

GP

, then

\log_{e} a^{n}, \log_{e} b^{n}, \log_{e} c^{n}

will be in

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

For any three positive real numbers

a, b

and

c

. If

9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c) .

Then

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

In an arithmetic progression, if the

k^{t h}

term is

5 k + 1

,

then the sum of first

100

terms is

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Let

a, b, c, d, e

be natural numbers in an arithmetic progression such that

a + b + c + d + e

is the cube of an integer and

b + c + d

is a square of an integer. The least possible value of the number of digits of

c

EASY

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

$Let S_{n} = 1 \cdot (n - 1) + 2 \cdot (n - 2) + 3 \cdot (n - 3) + \dots + (n - 1) \cdot 1, n ⩾ 4 .$

$The sum \sum_{n = 4}^{\infty} (\frac{2 S_{n}}{n!} - \frac{1}{(n - 2)!}) is equal to :$

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

R s . 720

was divided among

A, B, C, D

and

E

. The sum received by them was in ascending order and in Arithmetic Progression.

E

received

R s . 40

more than

A

. How much did

B

received?

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

What is the value of

21 + 24 + 27 + . . . . . + 51

How many three-digit numbers are divisible by $6$ in all?

Important Questions on Sequence and Series

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