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If $a, b, c, d$ are distinct integers in A.P. such that $d = a^{2} + b^{2} + c^{2}$ then $a + b + c + d$ is -

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Important Questions on Sequence and Series

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

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 :

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

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

MEDIUM

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

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

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

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

The number of terms in an

A . P .

is even, the sum of the odd terms in it is

24

and that the even terms is

30 .

If the last term exceeds the first term by

10 \frac{1}{2},

then the number of terms in the

A . P .

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

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___.

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

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

If the sum of the first

n

terms of the series

\sqrt{3} + \sqrt{75} + \sqrt{243} + \sqrt{507} + \dots

435 \sqrt{3},

then

n

equals:

MEDIUM

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

a^{1 / x} = b^{1 / y} = c^{1 / z}

and

a, b, c

are in geometrical progression, then

x, y, z

are in

MEDIUM

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Let

a_{1}, a_{2}, a_{3}, \dots \dots, a_{49}

be in

A . P .

such that

Σ_{k = 0}^{12} a_{4 k + 1} = 416

and

a_{9} + a_{43} = 66 .

a_{1}^{2} + a_{2}^{2} + \dots + a_{17}^{2} = 140 m,

then

m

is equal to:

HARD

Mathematics>Algebra>Sequence and Series>Arithmetic Progression

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than

200

and less than

220 .

If the second term in it is

12

, then its

4^{th}

term 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

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

MEDIUM

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:

If a, b, c, d are distinct integers in A.P. such that d=a2 + b2 + c2 then a + b + c + d is -

Important Questions on Sequence and Series

Learn and Prepare for any exam you want !

If $a, b, c, d$ are distinct integers in A.P. such that $d = a^{2} + b^{2} + c^{2}$ then $a + b + c + d$ is -