JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

a_r > 0, r \in N

and

a_1, a_2, a_3, \ldots . a_{2 n}

are in A.P., then

\frac{a_1+a_{2 n}}{\sqrt{a_1}+\sqrt{a_2}}+\frac{a_2+a_{2 n-1}}{\sqrt{a_2}+\sqrt{a_3}}+\frac{a_3+a_{2 n-2}}{\sqrt{a_3}+\sqrt{a_4}}+\ldots .+\frac{a_n+a_{n+1}}{\sqrt{a_n}+\sqrt{a_{n+1}}}

is equal to

View answer and explanation

Correct option: B

\frac{n\left(a_1+a_{2 n}\right)}{\sqrt{a_1}+\sqrt{a_{n+1}}}

Option B is correct because the given expression can be simplified using the properties of arithmetic progressions and then summed to obtain the final result.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

Given the sets

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

(ii)

A-(B \cap C)

(iii)

(B \cup C)-A

a,b,c

are in A.P.;

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

are in Suppose

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

, as

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

where

y=x-2

, then

\sum\limits_{{i=0}}^{2012} a_i

equals If

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

and

\log \left(\frac{a}{3 b}\right)

are in

A P

, where

a, b

and c are in

G P

, then

a, b, c

are the lengths of sides of If the sum of three numbers in G.P. is 63 and the product of the first and the second term is

\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is