EASY

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The heights of five runners are $160 cm$ , $137 cm$ , $149 cm$ , $153 cm$ and $161 cm$ respectively. Find the mean height per runner.

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Important Questions on Progression and Series

EASY

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

Let

a_{1}, a_{2}, {\dots . . a}_{10}

be a G.P. If

\frac{a_{3}}{a_{1}} = 25,

then

\frac{a_{9}}{a_{5}}

equals:

HARD

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

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

EASY

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The product of three consecutive terms of a

G . P .

512

. If

4

is added to each of the first and the second of these terms, the three terms now form an

A . P .

, then the sum of the original three terms of the given

G . P .

is :

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The sum of first

20

terms of the sequence

0.7, 0.77, 0.777, . . . . . .,

is :

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

y = \cos^{2} x + s e c^{2} x

, where

0 \leq x < \frac{π}{2}

, then which one of the following is correct?

HARD

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The number of real solutions of the equation

\sin^{- 1} (\sum_{i = 1}^{\infty} x^{i + 1} - x \sum_{i = 1}^{\infty} {(\frac{x}{2})}^{i}) = \frac{π}{2} - \cos^{- 1} (\sum_{i = 1}^{\infty} {(- \frac{x}{2})}^{i} - \sum_{i = 1}^{\infty} {(- x)}^{i})

lying in the interval

(- \frac{1}{2}, \frac{1}{2})

is____.

(Here, the inverse trigonometric functions

\sin^{- 1} x & \cos^{- 1} x

assume values in

[- \frac{π}{2}, \frac{π}{2}] & [0, π]

respectively.)

HARD

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

Let

b_{i} > 1

for

i = 1, 2, \dots ., 101 .

Suppose

\log_{e} b_{1}, \log_{e} b_{2}, \dots . ., \log_{e} b_{101}

are in Arithmetic Progression (A.P.) with the common difference

\log_{e} 2 .

Suppose

a_{1}, a_{2}, \dots ., a_{101}

are in A.P. such that

a_{1} = b_{1}

and

a_{51} = b_{51} .

t = b_{1} + b_{2} + \dots + b_{51}

and

s = a_{1} + a_{2} + \dots + a_{51}

, then

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

Let

C_{0}

be a circle of radius

1

. For

n \geq 1,

let

C_{n}

be a circle whose area equals the area of a square inscribed in

C_{n - 1}

. Then

(\sum_{u = 0}^{\infty} area (C_{i}))

equals,

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The arithmetic mean and the geometric mean of two positive numbers

p

and

q (p > q)

are

A

and

G

respectively. Which one of the following is correct?

EASY

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

Collect all the sequence of the five consecutive integers such that their product is equal to one of the least integer. Let $X$ be the collection of all possible such sequences. Let $P$ be the smallest integer and $Q$ be the largest integer in the sequences.

What is the arithmetic mean of $P and Q$ ?

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The sum of the

3^{r d}

and the

4^{t h}

terms of a

G . P .

60

and the product of its first three terms is

1000.

If the first term of this

G . P .

is positive, then its

7^{t h}

term is:

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

For

x > 0

, what is the minimum value of

x + \frac{x + 2}{2 x} ?

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The quotient when

1 + x^{2} + x^{4} + . . . + x^{34}

is divided by

1 + x + x^{2} + . . . + x^{17}

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

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

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

Let $S_{1}$ be the sum of areas of the squares whose sides are parallel to coordinate axes. Let $S_{2}$ be the sum of areas of the slanted squares as shown in the figure. Then $S_{1} / S_{2}$ is

Question Image

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

If three distinct numbers

a, b, c

are in G.P. and the equations

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

and

d x^{2} + 2 e x + f = 0

have a common root, then which one of the following statements is correct?

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

If the

2^{n d}, 5^{t h}

and

9^{t h}

terms of a non-constant arithmetic progression are in geometric progression, then the common ratio of this geometric progression is

EASY

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

What is the minimum value of

\cos^{3} θ + \sec^{3} θ

where

0^{o} \leq θ < 90^{o}

EASY

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The harmonic mean and the geometric mean of two numbers are

10 and 12

respectively. What is their arithmetic mean?

MEDIUM

Elementary Mathematics>Arithmetic>Progression and Series>A.M. and G.M.

The geometric mean of

x

and

y

6

and the geometric mean of

x, y

and

z

is also

6

. Then the value of

z

is:

The heights of five runners are 160 cm, 137 cm, 149 cm, 153 cm and 161 cm respectively. Find the mean height per runner.

Important Questions on Progression and Series

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The heights of five runners are $160 cm$ , $137 cm$ , $149 cm$ , $153 cm$ and $161 cm$ respectively. Find the mean height per runner.