Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 15

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Suppose that all the terms of an arithmetic progression ( $A . P .$ ) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is $6 : 11$ and the seventh term lies in between $130$ and $140$ , then the common difference of this $A . P .$ is

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Important Questions on Sequences and Series

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 16

Let

a_{1}, a_{2}, a_{3}, \dots

be terms of an

AP

. If

\frac{a_{1} + a_{2} + \dots + a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q

, then

\frac{a_{6}}{a_{21}}

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 17

If

a_{1}, a_{2}, \dots, a_{n}

are in

HP

, then the expression

a_{1} a_{2} + a_{2} a_{3} + \dots + a_{n - 1} a_{n}

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 18

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 19

A person is to count

4500

currency notes. Let

a_{n}

denote the number of notes he counts in the

n^{t h}

minute. If

a_{1} = a_{2} = \dots = a_{10} = 150

and

a_{10}

,

a_{11}, \dots

are in an

A . P .

with common difference

- 2

, then the time taken by him to count all notes is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 20

A man saves

Rs . 200

in each of the first three months of his service. In each of the subsequent months, his savings increases by

Rs . 40

more than the savings of immediately previous month. His total saving from the start of service will be

Rs . 11040

after

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 21

Let

a_{n}

be the

n^{th}

term of an A.P. If

\sum_{r = 1}^{100} a_{2 r} = α

and

\sum_{r = 1}^{100} a_{2 r - 1} = β,

then the common difference of the A.P. is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 22

The sum of first

20

terms of the sequence

0.7, 0.77, 0.777, . . .

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 23

If

{(10)}^{9} + 2 {(11)}^{1} {(10)}^{8} + 3 {(10)}^{2} {(10)}^{7} + \dots \dots + 10 {(11)}^{9} = k (10)^{9},

then

k

is equal to