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

100% studentsanswered this correctly

Important Questions on Sequences and Series

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 3

The mean of a set of observations is

\bar{x}

. If each observation is divided by

α \neq 0

, and then is increased by

10

, then the mean of the new set is ____.

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 4

Consider an

A . P .

with first term

' a'

and the common difference

d

. Let

S_{k}

denote the sum of the first

k

terms. Let

\frac{S_{k x}}{S_{x}}

is independent of

x

, then

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 5

\sum_{r = 1}^{\infty} (2 r - 1) {(\frac{9}{11})}^{r}

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 7

If

a, a_{1}, a_{2}, \dots \dots, a_{10}, b

are in A.P. and

a, g_{1}, g_{2}, \dots g_{10}, b

are in

G . P .

and

h

is the

H . M .

between

a

and

b

then

\frac{a_{1} + a_{2} + \dots . . + a_{10}}{g_{1} g_{10}} + \frac{a_{2} + a_{3} + \dots . . + a_{9}}{g_{2} g_{9}} + \dots \dots + \frac{a_{5} + a_{6}}{g_{5} g_{6}}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 8

The sum of the first

n

terms of the series

1^{2} + 2 \cdot 2^{2} + 3^{2} + 2 \cdot 4^{2} + 5^{2} + 2 \cdot 6^{2} + \dots \dots .

is

\frac{n (n + 1)^{2}}{2}

, when

n

is even. When

n

is odd, the sum is -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 11

The sum of the first

100

terms common to the series

17, 21, 25, \dots \dots \dots

and

16, 21, 26, \dots \dots \dots \dots . .

is

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 12

If

a, b, c

are positive such that

a b^{2} c^{3} = 64

then least value of

(\frac{1}{a} + \frac{2}{b} + \frac{3}{c})

is -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>EXERCISE-2>Q 13

If

a_{1}, a_{2}, \dots \dots \dots a_{n} \in R^{+}

and

a_{1} \cdot a_{2} \dots \dots a_{n} = 1

then the least value of

(1 + a_{1} + a_{1}^{2}) (1 + a_{2} + a_{2}^{2}) \dots . (1 + a_{n} + a_{n}^{2})

is -