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

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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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Important Questions on Sequences and Series

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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

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 24

Three positive numbers form an increasing G.P. If the middle term of the G.P. is doubled, then the new numbers are in A.P. Then the common ratio of the G.P. is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-3>Q 25

If

m

is the A.M. of two distinct real numbers

l

and

n (l, n > 1)

and

G_{1}, G_{2}

and

G_{3}

are three geometric means between

l

and

n

, then

G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}

equals