Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 18

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

The first term of an infinitely decreasing GP is unity and its sum is S. The sum of the squares of the terms of the progression is

50% studentsanswered this correctly

Important Questions on Sequences and Series

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 19

A particle begins at the origin and moves successively in the following manner as shown, $1$ unit to the right, $1 / 2$ unit up, $1 / 4$ unit to the right, $1 / 8$ unit down, $1 / 16$ unit to the right etc. The length of each move is half the length of the previous move and movement continues in the 'zigzag' manner indefinitely. The co-ordinates of the point to which the 'zigzag' converges is -

Question Image

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 20

Let

a_{n}

be the

n th

term of a

GP

of positive numbers. If

\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

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 21

If

p, q, r

in harmonic progression and

p & r

be different having same sign then the roots of the equation

p x^{2} + q x + r = 0

are

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 22

If

x > 1, y > 1, z > 1

are in GP, then

\frac{1}{1 + \ln x}, \frac{1}{1 + \ln y}

,

\frac{1}{1 + \ln z}

are in

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 23

If

ln (a + c), ln (c - a), ln (a - 2 b + c)

are in A.P., then

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 24

If the

(m + 1)^{t h}, (n + 1)^{t h} & (r + 1)^{t h}

terms of an AP are in GP

& m, n, r

are in H P, then the ratio of the common difference to the first term of the AP is -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 25

The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation,

2 x^{2} - 3 x + 5 = 0

is -

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-1>Q 26

If the sum of the first

n

natural numbers is

\frac{1}{5}

times the sum of the their squares, then the value of

n

is.