For distinct positive numbers a , b and c , if a 2 , b 2 and c 2 are in AP , then which one of the following triplets is also in AP ?

1 b + 2 c , 1 c + 2 a , 1 a + 2 b

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Let $a_{1}, a_{2}, a_{3}, \dots, a_{49}$ be in $A . P .$ such that $\sum_{k = 0}^{12} a_{4 k + 1} = 416$ and $a_{9} + a_{43} = 66$ . If $a_{1}^{2} + a_{2}^{2} + \dots + a_{17}^{2} = 140 m,$ then $m$ is equal to

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Important Questions on Sequences and Series

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 6

\cos^{4} θ \sec^{2} α, \frac{1}{2}

and

\sin^{4} θ {cosec}^{2} α

are in A.P., then

\cos^{8} θ \sec^{6} α, \frac{1}{2}

and

\sin^{8} θ {cosec}^{6} α

are in

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 7

A . P .

consist of even number of terms

2 n

having middle terms equal to

1

and

7

, respectively. If

n

is the maximum value which satisfy

t_{1} t_{2 n} + 713 \geq 0

, then the value of the first term of the series is

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 8

For

a, b & c \in R - {0}

, let

\frac{a + b}{1 - a b}, b, \frac{b + c}{1 - b c}

are in

A . P .

, if

α

and

β

are the roots of the quadratic equation

2 a c x^{2} + 2 a b c x + (a + c) = 0

, then the value of

(1 + α)

(1 + β)

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 9

In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored

23, 14, 11,

and

20

points, respectively. Her points per-game average was higher after nine games than it was after the first five games. Her average after ten games was greater than

18 .

What is the least number of points she could have scored in the tenth game?

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 10

A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have $3$ rows of small congruent equilateral triangles, with $5$ small triangles in the base row. Total $N$ number of toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of $2003$ small equilateral triangles. Then find the sum of all digits of $N .$

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 11

A B C

is a right-angled triangle in which

∠ B = 90 °

and

B C = a .

n

points

L_{1}, L_{2}, \dots \dots, L_{n}

A B

is divided in

n + 1

equal parts and

L_{1} M_{1}, L_{2} M_{2}, \dots \dots L_{n} M_{n}

are line segments parallel to

B C

and

M_{1}, M_{2}, \dots \dots \dots . M_{n}

are on

A C,

then the sum of the lengths of

L_{1}^{} M_{1}, L_{2} M_{2}, \dots . . L_{n} M_{n}

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 12

\tan \frac{2 π}{18}, x

and

\tan \frac{7 π}{18}

are in A.P. and

\tan \frac{2 π}{18}, y

and

\tan \frac{5 π}{18}

are in A.P., then the value of

\frac{x}{y}

will be

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Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 2>Q 13

Given the sequence of numbers

x_{1}, x_{2}, x_{3}, x_{4}, \dots, x_{2005}

which satisfy

\frac{x_{1}}{x_{1} + 1} = \frac{x_{2}}{x_{2} + 3} = \frac{x_{3}}{x_{3} + 5} = \dots = \frac{x_{2005}}{x_{2005} + 4009}

, the nature of the sequence is

Let a1, a2, a3,…, a49 be in A.P. such that∑k=012a4k+1=416 and a9+a43=66. If a12+a22+…+a172=140m, then m is equal to

Important Questions on Sequences and Series

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Let $a_{1}, a_{2}, a_{3}, \dots, a_{49}$ be in $A . P .$ such that $\sum_{k = 0}^{12} a_{4 k + 1} = 416$ and $a_{9} + a_{43} = 66$ . If $a_{1}^{2} + a_{2}^{2} + \dots + a_{17}^{2} = 140 m,$ then $m$ is equal to