Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 38

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There are $n$ A.M.'s between $3$ and $54,$ such that the $8$ th mean: $(n - 2)^{th}$ mean: $3 : 5$ . The value of $n$ 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-1>Q 39

The third term of a G.P is

4

, then the product of the first five terms is _____

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 40

If

S

be the sum to infinity of a G.P., whose first term is

a

, then the sum of first

n

terms is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 41

For a sequence

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

and

\frac{a_{n + 1}}{a_{n}} = \frac{1}{3} .

Then

\sum_{r = 1}^{20} a_{r}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 42

α, β

be the roots of the equation

x^{2} - 3 x + a = 0

and

γ, δ

the roots of

x^{2} - 12 x + b = 0

and numbers

α, β, γ, δ

(in this order) form an increasing G.P., then

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 43

One side of an equilateral triangle is

24 cm

. The mid-points of its sides are joined to form another triangle whose mid-points are in turn joined to form still another triangle. This process continues indefinitely. Then the sum of the perimeters of all the triangles is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 44

Let the positive numbers

a, b, c, d

be in A.P. Then

a b c, a b d, a c d, b c d

are

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 45

If

3 + \frac{1}{4} (3 + d) + \frac{1}{4^{2}} (3 + 2 d) + \dots \dots +

upto

\infty = 8,

then the value of

d

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-1>Q 46

STATENENT-1 : $3, 6, 12$ are in G.P., then $9, 12, 18$ are in H.P.

STATEMENT-2 : If three consecutive terms of a G.P. are positive and if middle term is added in these terms, then resultant will be in H.P.