Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 39

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If $\frac{a_{k + 1}}{a_{k}}$ is constant for every $k \geq 1 .$ If $n > m \Rightarrow a_{n} > a_{m}$ and $a_{1} + a_{n} = 66, a_{2} a_{n - 1} = 128$ and $\sum_{i = 1}^{n} a_{i} = 126$ , then

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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-2>Q 40

The sides of a right triangle form a G.P., the tangent of the smallest angle is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 41

If

b_{1}, b_{2}, b_{3} (b_{i} > 0)

are three successive terms of a G.P. with common ratio

r,

the value of

r

for which the inequality

b_{3} > 4 b_{2} - 3 b_{1}

holds is given by

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 42

If

a

satisfies the equation

a^{2017} - 2 a + 1 = 0

and

S = 1 + a + a^{2} + \dots . . + a^{2016}

, then possible value(s) of

S

is/are

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 43

Let

a,

x, b

be in A.P.,

a, y, b

be in G.P. and

a, z, b

be in H.P. If

x = y + 2

and

a = 5 z,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 44

Which of the following is/are TRUE?

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 45

If the arithmetic mean of two positive numbers

a & b (a > b)

is twice their geometric mean, then

a : b

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 46

If

\sum_{i = 1}^{n} r (r + 1) (2 r + 3) = a n^{4} + b n^{3} + c n^{2} + d n + e,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 5 - Sequences and Series>Exercise-2>Q 47

The value of

\sum_{r = 1}^{n} \frac{1}{\sqrt{a + r x} + \sqrt{a + (r - 1) x}}

is