Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 59

EASY

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IMPORTANT

Earn 100

The $15 t h$ term of the series $2 \frac{1}{2} + 1 \frac{7}{3} + 1 \frac{1}{9} + \frac{20}{23} + . . .$ is

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Important Questions on Progression and Series

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 60

If

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

are in H.P., then

\frac{a_{1}}{a_{2} + a_{3} + . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . + a_{n}}, . . ., \frac{a_{n}}{a_{1} + a_{2} + . . + a_{n - 1}}

are in

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 61

If

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

are in H.P. 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)}, . . . ., \frac{a_{n}}{f (n)}

are in

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 62

If

a, b, c

are in A.P., then

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

will be in

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 63

If

a, b,

and

c

are in A.P.,

p, q,

and

r

are in H.P., and

a p, b q,

and

c r

are in G.P. then

\frac{p}{r} + \frac{r}{p}

is equal to

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 64

a, b, c, d \in R^{+}

such that

a, b,

and

c

are in A.P. and

b, c

and

d

are in H.P., then

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 65

If in a progression

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

etc.,

(a_{r} - a_{r + 1})

bears a constant ratio with

a_{r} \times a_{r + 1}

, then the terms of the progression are in

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 66

If

a, b,

and

c

are in G.P. then

a + b, 2 b,

and

b + c

are in

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 67

If

a, x

and

b

are in

AP

,

a, y,

and

b

are in

GP

, and

a, z, b

are in

HP

such that

x = 9 z

and

a > 0, b > 0

, then