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

EASY

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IMPORTANT

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Consider an A.P., $a_{1}, a_{2}, a_{3}, . . . .$ such that $a_{3} + a_{5} + a_{8} = 11$ and $a_{4} + a_{2} = - 2,$ then the value of $a_{1} + a_{6} + a_{7}$ is

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Important Questions on Progression and Series

EASY

JEE Main/Advance

IMPORTANT

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

If

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

are in, then

a_{p}, a_{q}, a_{r}

are in

AP

if

p, q, r

are in

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 11

Let

α, β \in R .

If

α, β^{2}

are the roots of quadratic equation

x^{2} - p x + 1 = 0

and

α^{2}, β

are the roots of quadratic equation

x^{2} - q x + 8 = 0,

then the value of

r

if

\frac{r}{8}

is the arithmetic mean of

p

and

q

, is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 12

If the sum of

m

terms of an A.P., is the same as the sum of its

n

terms, then the sum of its

(m + n)

terms is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 13

If $S_{n}$ denotes the sum of $n$ terms of A.P., then, $S_{n + 3} - 3 S_{n + 2} + 3 S_{n + 1} - S_{n}$ is equal to

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 14

In an A.P. of which

a

is the first term, if the sum of the first

p

terms is zero, then the sum of the next

q

terms is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 15

If

S_{n}

denotes the sum of first

n

terms of an A.P. and

\frac{S_{3 n} - S_{n - 1}}{S_{2 n} - S_{2 n - 1}} = 31

,then the value of

n

is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 16

The number of terms of an A.P., is even; the sum of the odd terms is

24

, and of the even terms is

30

, and the last term exceeds the first by

\frac{21}{2}

, then the number of terms in the series is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 5 - Progression and Series>Exercises>Q 17

Let

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

be terms of an A.P. If

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

, then

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

equals