Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 16

MEDIUM

NDA & NA EE

IMPORTANT

Earn 100

The value of $x + y + z$ is $15$ , if $a, x, y, z, b$ are in A.P. while the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is $\frac{5}{3}$ . If $a, x, y, z, b$ are in H.P., then $a$ and $b$ are

50% studentsanswered this correctly

Important Questions on Sequence and Series

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 17

Given that

{(m + 1)}^{th}, {(n + 1)}^{th}

and

{(r + 1)}^{th}

terms of an A.P. are in G.P. and

m, n, r

are in H.P., then the ratio of the first term of the A.P. to its common difference in terms of

n

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 18

If the

m^{th}

and

n^{th}

term of a H.P. are

n

and

m

respectively, then the

{m n}^{th}

term is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 19

Two AM's

A_{1}

and

A_{2}

, two GM's

G_{1}

and

G_{2}

and two HM's

H_{1}

and

H_{2}

are inserted between any two numbers, then

H_{1}^{- 1} + H_{2}^{- 1}

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 20

Which term of the sequence

20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \dots

is the first negative term?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 21

If

p

times the

p^{th}

term of an A.P. is

q

times the

q^{th}

term, then what is the

{(p + q)}^{th}

term equal to?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 22

If

a, 2 a + 2, 3 a + 3

are in G.P., then what is the fourth term of the G.P.?

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 23

If

\frac{a^{n + 1} + b^{n + 1}}{a^{n} + b^{n}}

is the arithmetic mean between

a

and

b

, then

n

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 8 - Sequence and Series>PRACTICE EXERCISE>Q 24

Let

a, b, c

be three positive real numbers such that their product is unity, then the least value of

(1 + a) (1 + b) (1 + c)

is