EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Sequence and Series>IOQM - PRMO and RMO 2019 (11-08-2019)>Q 1

EASY

IOQM - PRMO and RMO

IMPORTANT

Earn 100

Let $x_{1}$ be a positive real number and for every integer $n \geq 1$ let $x_{n + 1} = 1 + x_{1} x_{2} \dots x_{n - 1} x_{n} .$ If $x_{5} = 43,$ what is the sum of digits of the largest prime factor of $x_{6}$ ?

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Important Questions on Sequence and Series

EASY

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Sequence and Series>IOQM - PRMO and RMO 2019 (11-08-2019)>Q 1

Let

x_{1}

be a positive real number and for every integer

n \geq 1

let

x_{n + 1} = 1 + x_{1} x_{2} \dots x_{n - 1} x_{n} .

If

x_{5} = 43,

what is the sum of digits of the largest prime factor of

x_{6}

?

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Sequence and Series>IOQM - PRMO and RMO 2019 (11-08-2019)>Q 2

A natural number

k > 1

is called good if there exist natural numbers

a_{1} < a_{2} < \dots < a_{k}

such that

\frac{1}{\sqrt{a_{1}}} + \frac{1}{\sqrt{a_{2}}} + \dots + \frac{1}{\sqrt{a_{k}}} = 1

. Let

f (n)

be the sum of the first

n

good numbers,

n \geq 1

. Find the sum of all values of

n

for which

\frac{f (n + 5)}{f (n)}

is an integer.

EASY

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Sequence and Series>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 3

Consider the set

E

of all positive integers

n

such that when divided by

9, 10, 11

, respectively, the remainders (in that order) are all

> 1

and form a non-constant geometric progression. If

N

is the largest element of

E

, then find

\frac{N}{4}

.

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Sequence and Series>IOQM - PRMO and RMO 2018>Q 4

Let

N = 6 + 66 + 666 . + \dots + 666 \dots 66,

where there are hundred

6' s

in the last term in the sum. How many times does the digit

7

occur in the number

N

?