If the sum to infinity of the series $1+4 x+7 x^2+10 x^3+\ldots \ldots \ldots$ is $\frac{35}{16}$, where $|x|<1$ then ${x}$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

If the sum to infinity of the series

1+4 x+7 x^2+10 x^3+\ldots \ldots \ldots

\frac{35}{16}

, where

|x|<1

then

{x}

is equal to

View answer and explanation

Correct option: B

\frac{1}{5}

Option B (

\frac{1}{5}

) is correct because it solves for x using the sum to infinity formula for an arithmetico-geometric 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}