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If $2 . n_{P_{1}}, n_{P_{2}}, n_{P_{3}}$ are three consecutive terms of an $AP$ then they are

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Important Questions on Sequence and Series

HARD

Mathematics>Algebra>Sequence and Series>Harmonic 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>Harmonic Progression

If $m$ is the $A . M .$ of two distinct real numbers $I$ and $n$ $(I, n > 1)$ and $G_{1}, G_{2} and G_{3}$ are three geometric means between $I and n$ , then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic Progression

Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then

\frac{a}{c}

is equal to:

HARD

Mathematics>Algebra>Sequence and Series>Harmonic 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>Harmonic Progression

a > 1, b > 1

and

c > 1

are in geometric progression, then

\frac{1}{1 + \log_{e} a}, \frac{1}{1 + \log_{e} b}, \frac{1}{1 + \log_{e} c}

will be in

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic 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.

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic 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>Harmonic 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>Sequence and Series>Harmonic Progression

a, b, c

are in arithmetic progression, then

\frac{a}{b c}, \frac{1}{c}, \frac{2}{b}

will be in

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic Progression

x, y, z

are in

HP

, then

\log (x + z) + \log (x - 2 y + z)

is equal to

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic 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 :

HARD

Mathematics>Algebra>Sequence and Series>Harmonic Progression

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

are in

HP

and

f (k) = \sum_{r = 1}^{n} a_{r} - a_{k}

, then

\frac{a_{1}}{f (1)}, \frac{a_{2}}{f (2)}, \frac{a_{3}}{f (3)}, \dots, \frac{a_{n}}{f (n)}

are in

HARD

Mathematics>Algebra>Sequence and Series>Harmonic Progression

Let

α and β

be the roots of equation

p x^{2} + q x + r = 0

p \neq 0

. If

p, q, r

are in A.P. and

\frac{1}{α} + \frac{1}{β} = 4

, then the value of

|α - β|

HARD

Mathematics>Algebra>Sequence and Series>Harmonic 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>Sequence and Series>Harmonic 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>Harmonic 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

HARD

Mathematics>Algebra>Sequence and Series>Harmonic 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

EASY

Mathematics>Algebra>Sequence and Series>Harmonic Progression

\frac{(b + c - a)}{a}, \frac{(c + a - b)}{b}, \frac{(a + b - c)}{c}

are in

AP

, then

a, b, c

are in

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic Progression

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

, where

x, y, z

are unequal positive numbers and

a, b, c

are in

GP

, then

MEDIUM

Mathematics>Algebra>Sequence and Series>Harmonic Progression

\cos (x - y), \cos x

and

\cos (x + y)

are in

HP

, then

\cos x \sec (y / 2)

is equal to

If 2. nP1, nP2, nP3 are three consecutive terms of an AP then they are

Important Questions on Sequence and Series

Learn and Prepare for any exam you want !

If $2 . n_{P_{1}}, n_{P_{2}}, n_{P_{3}}$ are three consecutive terms of an $AP$ then they are