Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 33

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If $a, b,$ and $c$ are in G.P. and $x, y,$ respectively are the arithmetic means between $a, b$ and $b, c$ , then the value of $\frac{a}{x} + \frac{c}{y}$ is

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Important Questions on Progression and Series

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 34

If

a, b,

and

c

are in A.P.and

p

and

p'

are respectively, A.M. and G.M. between

a & b

while

q & q'

are respectively the AM and GM between

b & c

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 35

If

(1 + x) (1 + x^{2}) (1 + x^{4}) . . . (1 + x^{128}) = \sum_{r = 0}^{n} x^{r},

then

n

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 36

If

(1 - p) (1 + 3 x + 9 x^{2} + 27 x^{3} + 81 x^{4} + 243 x^{5}) = 1 - p^{6}, p \neq 1,

then the value of

\frac{p}{x}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 37

Consider the ten numbers

a r, a r^{2}, a r^{3}, . . ., a r^{10} .

If their sum is

18

and the sum of their reciprocals is

6

, then the product of these ten numbers is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 38

If $x, y,$ and $z$ are distinct prime numbers, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 39

Let $a = 1 1 1 . . . 1 (55 digits), b = 1 + 10 + 10^{2} + . . . + 10^{4},$

$c = 1 + 10^{5} + 10^{10} + 10^{15} + . . . + 10^{50},$ then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 40

Let

a_{n}

be the

n t h

term of a G.P. of positive numbers. Let

\sum_{n = 1}^{100} a_{2 n} = α

and

\sum_{n = 1}^{100} a_{2 n - 1} = β,

such that

α \neq β,

then the common ratio is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 41

The sum of

20

terms of a series of which every even term is

2

times the term before it and every odd term is

3

times the term before it, the first term being unity is