Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 2

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If the sum of $n$ terms of an A.P., is given by $S_{n} = a + b n + c n^{2},$ where $a, b, c$ are independent of $n$ , then

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Important Questions on Progression and Series

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 3

If

a, b, c

and

d

are four unequal positive numbers which are in A.P., then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 4

Which of the following can be terms (not necessarily consecutive) of any A.P.?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 5

In an arithmetic progression whose first term is

α

and common difference is

β; α, β \neq 0

, the ratio

r

of the sum of the first

n

terms to the sum of

n

terms succeeding them, does not depend on

n

. Then which of the following is/are correct?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 6

If

a^{2} + 2 b c, b^{2} + 2 c a, c^{2} + 2 a b

are in A.P. then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 7

If sum of an infinite G.P.

p, 1, 1 / p, 1 / p^{2}, . . . . .

is equal to

9 / 2

, then value of

p

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 8

The terms of an infinitely decreasing G.P. having common ratio

r

in which all the terms are positive, the first term is

4

, and the difference between the third and fifth terms is

\frac{32}{81}

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 9

Let

a_{1}, a_{2}, a_{3}, . . . . a_{n}

be in G.P. such that

3 a_{1} + 7 a_{2} + 3 a_{3} - 4 a_{5} = 0

. Then common ratio of G.P. can be

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 10

If

p (x) = \frac{1 + x^{2} + x^{4} + . . . + x^{2 n - 2}}{1 + x + x^{2} + . . . . + x^{n - 1}}

is a polynomial in

x

, then

n

can be