Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 5

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IMPORTANT

Earn 100

If $A$ be an arithmetic mean between two numbers and $S$ be the sum of $n$ arithmetic means between the same numbers, then

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Important Questions on Sequences and Series

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 6

Given that

n

number of

A . M' s

are inserted between two sets of numbers

a,

2 b

and

2 a, b

where

a, b \in R

. Suppose further that the

m^{t h}

means between these sets of numbers are same, then the ratio

a : b

equals

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 7

If the sum of first

n

terms of two

A P^{'} s

are in the ratio

3 n + 8 : 7 n + 15

, then the ratio of their

12^{t h}

terms is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 8

A circle with area

A_{1}

is contained in the interior of a larger circle with area

A_{1} + A_{2}

. If the radius of the larger circle is

3

, and if

A_{1}, A_{2}, A_{1} + A_{2}

is an arithmetic progression, and the radius of the smaller circle is given by

r

. Find

r^{2}

.

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 9

If the average of

20

different positive integers is

20

then the greatest possible number among these

20

numbers can be

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 10

The sequence

\log_{12} 162, \log_{12} x, \log_{12} y, \log_{12} z, \log_{12} 1250

is an arithmetic progression. What is

\frac{x}{10} ?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 11

In the sequence

2001, 2002, 2003,

..... each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is

2001 + 2002 - 2003 = 2000 .

What is the

2004^{th}

term in this sequence?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 12

The first four terms of an arithmetic sequence are

p, 9, (3 p - q)

and

(3 p + q)

. What is the sum of digits of the

2010^{th}

term of the sequence?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 25 - Sequences and Series>Level 1>Q 13

The number of terms in an

AP

(Arithmetic Progression) is even. The sums of the odd- and even-numbered terms are

24

and

30

, respectively. If the last term exceeds the first by

10.5

, the number of terms in the

AP

is