If a , b , c are in A . P . and A , B , C are in G . P . (common ratio ≠ 1 ), then which of the following is/are correct?

A 2 a , B 2 b , C 2 c are in H . P . , if common ratio of G . P . is c a

If A a , B b , C c are in H . P . , then common ratio of GP is a c .

If A 2 a , B 2 b , C 2 c are in H . P . , then common ratio of G . P . is a c

If a , b , c are in A . P . and A , B , C are in G . P . (common ratio ≠ 1 ), then which of the following is/are correct?

A 2 a , B 2 b , C 2 c are in H . P . , if common ratio of G . P . is c a

HARD

Earn 100

If $a, b, c$ are in $A . P .$ and $A, B, C$ are in $G . P .$ (common ratio $\neq 1$ ), then which of the following is/are correct?

50% studentsanswered this correctly

Important Questions on Sequences and Series

MEDIUM

Mathematics>Algebra>Sequences 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

HARD

Mathematics>Algebra>Sequences 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

MEDIUM

Mathematics>Algebra>Sequences 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>Sequences 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:

MEDIUM

Mathematics>Algebra>Sequences 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>Sequences 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 :

HARD

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

Let

S_{n} = Σ_{k = 1}^{4 n} {(- 1)}^{\frac{k (k + 1)}{2}} k^{2}

. Then

S_{n}

can take value(s)

HARD

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

Let

A P (a; d)

denote the set of all the terms of an infinite arithmetic progression with first term

a

and common difference

d > 0 .

A P (1; 3) \cap A P (2; 5) \cap A P (3; 7) = A P (a; d)

then

a + d

equals ____

HARD

Mathematics>Algebra>Sequences 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 :

MEDIUM

Mathematics>Algebra>Sequences 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>Sequences and Series>Arithmetic Progression

Let

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

,be in A.P. If

a_{3} + a_{7} + a_{11} + a_{15} = 72

, then the sum of its first

17

terms is equal to :

HARD

Mathematics>Algebra>Sequences 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___.

MEDIUM

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

The number of terms common to the two A.P.’s

3, 7, 11, \dots, 407

and

2, 9, 16, \dots, 709

is ____________.

HARD

Mathematics>Algebra>Sequences 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 .

MEDIUM

Mathematics>Algebra>Sequences 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:

MEDIUM

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

Let

a_{1}, a_{2}, a_{3} . . .

be an

A . P .

with

a_{6} = 2 .

Then, the common difference of this

A . P .,

which maximise the product

a_{1} \cdot a_{4} \cdot a_{5},

is :

HARD

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

The sum of all natural numbers

n

such that

100 < n < 200

and

H . C . F .

(91, n) > 1

MEDIUM

Mathematics>Algebra>Sequences 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

MEDIUM

Mathematics>Algebra>Sequences 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.

HARD

Mathematics>Algebra>Sequences and Series>Arithmetic Progression

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

and

^{n} C_{6}

are in A.P., then

n

can be

If a,b,c are in A.P. and A,B,C are in G.P. (common ratio ≠1 ), then which of the following is/are correct?

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

If $a, b, c$ are in $A . P .$ and $A, B, C$ are in $G . P .$ (common ratio $\neq 1$ ), then which of the following is/are correct?