JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Let

b_i>1

for

i=1,2, \ldots, 101

. Suppose

\log _e b_1

\log _e b_2, \ldots, \log _e b_{101}

are in Arithmetic Progression (A.P) with the common difference

{\log _e}2

. Suppose

a_1, a_2, \ldots, a_{101}

are in A.P. such that

a_1=b_1

and

a_{51}=b_{51}

. If

t=b_1+b_2+\ldots+b_{51}

and

s=a_1+a_2+\ldots+a_{51}

, then

View answer and explanation

Correct option: B

s>t

and

a_{101} < b_{101}

Option B (

s>t

and

a_{101} < b_{101}

) is correct because the sum of the arithmetic progression is greater than the sum of the geometric progression, while the 101st term of the arithmetic progression is less than the 101st term of the geometric progression.

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