MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 3

MEDIUM

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IMPORTANT

Earn 100

Let the sum of $n, 2 n, 3 n$ terms of an A.P. be $S_{1}, S_{2}$ and $S_{3}$ respectively, show that $S_{3} = 3 (S_{2} - S_{1})$

Important Questions on Sequences and Series

MEDIUM

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 4

Find the sum of all numbers between

200

and

400

which are divisible by

7

.

HARD

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 5

Find the sum of integers from

1

to

100

that are divisible by

2

or

5 .

MEDIUM

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 6

Find the sum of all two-digit numbers which when divided by

4,

yields

1

as remainder.

MEDIUM

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 7

If

f

is a function satisfying

f (x + y) = f (x) . f (y)

for all

x, y \in N

, such that

f (1) = 3

and

Σ_{1}^{n} f (x) = 120

, find the value of

n .

MEDIUM

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 8

The sum of some terms of

G . P .

is

315

whose first term and the common ratio are

5

and

2

, respectively. Find the last term and the number of terms.

EASY

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IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 9

The first term of a

G . P .

is

1

. The sum of the third term and fifth term is

90

. Find the common ratio of

G . P .

MEDIUM

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IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 10

The sum of three numbers in

G . P

. is

56

. If we subtract

1, 7, 21

from these numbers

n

in that order, we obtain an arithmetic progression. Find the numbers.

HARD

11th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class XI>Chapter 9 - Sequences and Series>Miscellaneous Exercise on Chapter 9>Q 11

A G.P. consists of an even number of terms. If the sum of all the terms is

5

times the sum of terms occupying odd places, then find its common ratio.