JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Medium

1 of 1

Analyzing +4 | -1

a,{a_1},{a_2}, \ldots ,{a_{2n}},b

are in arithmetic progression and

a,{g_1},{g_2}, \ldots ,{g_{2n}},b

are in geometric progression and

h

is the harmonic mean of

a

and

b

, then

\frac{{{a_1} + {a_{2n}}}}{{{g_1}{g_{2n}}}} + \frac{{{a_2} + {a_{2n - 1}}}}{{{g_2}{g_{2n - 1}}}} + ... + \frac{{{a_n} + {a_{n + 1}}}}{{{g_n}{g_{n + 1}}}}

is equal to

View answer and explanation

Correct option: D

\frac{{2n}}{h}

Option D (

\frac{{2n}}{h}

) is correct because by properties of AP and GP, the expression simplifies to a constant term involving the harmonic mean.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

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

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

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

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

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

y

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

y=x-2

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

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

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

A P

a, b

G P

a, b, c

\frac{3}{4}