Let a , b & c be in A.P. with a common difference d . Then e 1 c , e b a c , e 1 a are in

G.P. with common ratio e d b 2 - d 2

HARD

Earn 100

The sum of $3$ numbers of a $GP$ is $39$ and their product is $729$ . The numbers are

62.5% studentsanswered this correctly

Important Questions on Progression and Series

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

In the sequence

25, 5, 1, \dots, \frac{1}{3125}

which term is

\frac{1}{3125}

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

a, b, c

are in G.P., then

\frac{a - b}{b - c}

is equal to:

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Given

A = 2^{65}

and

B = (2^{64} + 2^{63} + 2^{62} + \dots + 2 °)

, which of the following is true?

HARD

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

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

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Let

a, b & c

be in A.P. with a common difference

d

. Then

e^{\frac{1}{c}}, e^{\frac{b}{a c}}, e^{\frac{1}{a}}

are in

HARD

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

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

HARD

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \dots

upto

\infty = \frac{π^{2}}{6}

, then value of

\frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + \dots

upto

\infty

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

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

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

In an ordered set of four numbers, the first

3

are in

AP

and the last

3

are in

GP

whose common ratio is

\frac{7}{4}

. If the product of the first and fourth of these number is

49

, then the product of the second and third of these, is

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

If $0 < x < 1,$ then $\frac{3}{2} x^{2} + \frac{5}{3} x^{3} + \frac{7}{4} x^{4} + \dots,$ is equal to

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

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:

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

The third term of a

G . P .

9

. The product of its first five terms is

HARD

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

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.)

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Three numbers is

G . P .

with their sum is

130

and their product is

27, 000

are _________

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

The sum of first

20

terms of the sequence

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

is :

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Suppose

p, q, r

are real numbers such that

q = p (4 - p), r = q (4 - q), p = r (4 - r) .

The maximum possible value of

p + q + r

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Three positive numbers form an increasing

G . P .

If the middle term in this

G . P .

is doubled, the new numbers are in

A . P .

Then the common ratio of the

G . P .

is :

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

If for

x, y \in R, x > 0,

y = \log_{10} x + \log_{10} x^{1 / 3} + \log_{10} x^{1 / 9} + \dots

upto

\infty

terms and

\frac{2 + 4 + 6 + \dots + 2 y}{3 + 6 + 9 + \dots + 3 y} = \frac{4}{\log_{10} x},

then the ordered pair

(x, y)

is equal to

EASY

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}

and

a, b, c

are in

G . P .

, then

x, y, z

will be in

MEDIUM

Quantitative Aptitude>Arithmetic>Progression and Series>Geometric Progression

Let

a_{1}, a_{2}, a_{3}, \dots

, be a

G . P .

such that

a_{1} < 0, a_{1} + a_{2} = 4

and

a_{3} + a_{4} = 16

. If

\sum_{i = 1}^{9} a_{i} = 4 λ

, then

λ

is equal to

The sum of 3 numbers of a GP is 39 and their product is 729 . The numbers are

Important Questions on Progression and Series

Learn and Prepare for any exam you want !

The sum of $3$ numbers of a $GP$ is $39$ and their product is $729$ . The numbers are