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If $a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225$ , then the sum of the first $24$ terms of the arithmetic progression $a_{1}, a_{2}, a_{3} . . . . .$ is equal to

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Important Questions on Sequences and Series

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Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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

and

^{n} C_{6}

are in A.P., then

n

can be

HARD

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

For

k \in N,

let

\frac{1}{α (α + 1) (α + 2) \dots \dots . (α + 20)} = \sum_{K = 0}^{20} \frac{A_{k}}{α + k},

where

α > 0 .

Then the value of

100 {(\frac{A_{14} + A_{15}}{A_{13}})}^{2}

is equal to ____________.

MEDIUM

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Basics of Sequence and Series

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>Basics of Sequence and Series

The sum of the series

\frac{1}{x + 1} + \frac{2}{x^{2} + 1} + \frac{2^{2}}{x^{4} + 1} + \dots + \frac{2^{100}}{x^{2^{100}} + 1}

when

x = 2

is:

EASY

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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

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

MEDIUM

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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>Basics of Sequence and Series

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:

HARD

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

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>Sequences and Series>Basics of Sequence and Series

The sum of all tree digit numbers which are odd is ?

MEDIUM

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

The value of

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

EASY

Mathematics>Algebra>Sequences and Series>Basics of Sequence and Series

For a sequence, if

S_{n} = \frac{5^{n} - 2^{n}}{2^{n}},

then its fourth term is

If a1+a5+a10+a15+a20+a24=225, then the sum of the first 24 terms of the arithmetic progression a1, a2, a3..... is equal to

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

If $a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225$ , then the sum of the first $24$ terms of the arithmetic progression $a_{1}, a_{2}, a_{3} . . . . .$ is equal to