JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

a_1, a_2, a_3, \ldots, a_n

are in H.P. and

f(k)=\sum\limits_{{r=1}}^n\left(a_r-a_k\right)

, then

\frac{a_1}{f(1)}, \frac{a_2}{f(2)}, \ldots, \frac{a_n}{f(n)}

, are in

View answer and explanation

Correct option: C

H.P.

Option C is correct because the reciprocals of terms in a Harmonic Progression (H.P.) form an Arithmetic Progression (A.P.), and manipulating the given expression using this property leads to the conclusion that the given terms are in H.P.

More Questions from SEQUENCE OF SERIES

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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