Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 15

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IMPORTANT

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If $S_{n}$ denotes the sum of first $n$ terms of an A.P. and $\frac{S_{3 n} - S_{n - 1}}{S_{2 n} - S_{2 n - 1}} = 31$ ,then the value of $n$ is

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Important Questions on Progression and Series

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 16

The number of terms of an A.P., is even; the sum of the odd terms is

24

, and of the even terms is

30

, and the last term exceeds the first by

\frac{21}{2}

, then the number of terms in the series is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 17

Let

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

be terms of an A.P. If

\frac{a_{1} + a_{2} + . . . + a_{p}}{a_{1} + a_{2} + . . . + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q

, then

\frac{a_{6}}{a_{21}}

equals

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 18

Concentric circles of radii

1, 2, 3, . . ., 100 cm

are drawn. The interior of the smallest circle is coloured red and the angular regions are coloured alternately green and red, so that no two adjacent regions are of the same colour. Then, the total area to the green regions in sq. cm is equal

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 19

If

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

are in A.P., then

\frac{a_{2 n + 1} - a_{1}}{a_{2 n + 1} + a_{1}} + \frac{a_{2 n} - a_{2}}{a_{2 n} + a_{2}} + . . . + \frac{a_{n + 2} - a_{n}}{a_{n + 2} + a_{n}}

is equal to

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 20

If

a_{1}, a_{2}, . . ., a_{n}

are in A.P. with common difference

d \neq 0,

then the sum of the series

\sin d [s e c a_{1} s e c a_{2} + s e c a_{2} s e c a_{3} + . . . + s e c a_{n - 1} s e c a_{n}]

is

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 21

A B C

is a right-angled triangle in which

∠ B = 90 °

and

B C = a .

If

n

points

L_{1}, L_{2}, . . ., L_{n}

on

A B

is divided in

n + 1

equal parts and

L_{1} M_{1}, L_{2} M_{2}, . . ., L_{n} M_{n}

are line segments parallel to

B C

and

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

are on

A C,

then the sum of the lengths of

L_{1} M_{1}, L_{2} M_{2}, . . . ., L_{n} M_{n}

is

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 22

If

a, b, c, d

are in G.P., then

{(b - c)}^{2} + {(c - a)}^{2} + {(d - b)}^{2}

is equal to

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 23

Let

\{t_{2}\}

be a sequence of integers in

GP

. in which

t_{4} : t_{6} = 1 : 4

and

t_{2} + t_{5} = 216 .

Then

t_{1}

is