Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Consider an infinite geometric series with first term $a$ and common ratio $r$ . If its sum is 4 and the second term is 3/4, then

$a = \frac{4}{7}, r = \frac{3}{7}$
$a = 2, r = \frac{3}{8}$
$a = \frac{3}{2}, r = \frac{1}{2}$
$a = 3, r = \frac{1}{4}$

The correct answer is: $a equals 3 comma blank r equals fraction numerator 1 over denominator 4 end fraction$

Sum is 4 and second term is ¾. It is given that first term is $a$ and common ratio is $r$ . Hence,
$fraction numerator a over denominator 1 minus r end fraction equals 4$ and $a r equals 3 divided by 4 blank rightwards double arrow r equals fraction numerator 3 over denominator 4 a end fraction$
Therefore,
$fraction numerator a over denominator 1 minus fraction numerator 3 over denominator 4 a end fraction end fraction equals 4 blank rightwards double arrow fraction numerator 4 a to the power of 2 end exponent over denominator 4 a minus 3 end fraction equals 4$
$rightwards double arrow a to the power of 2 end exponent minus 4 a plus 3 equals 0$
$rightwards double arrow open parentheses a minus 1 close parentheses open parentheses a minus 3 close parentheses equals 0$
$rightwards double arrow a equals 1$ or $3$
When $a equals 1 comma blank r equals 3 divided by 4$ and when $a equals 3 comma blank r equals 1 divided by 4$

Related Questions to study

$stack lim with n rightwards arrow infinity below invisible function application not stretchy sum from r equals 1 to n of fraction numerator r over denominator 1 cross times 3 cross times 5 cross times 7 cross times 9 cross times midline horizontal ellipsis cross times left parenthesis 2 r plus 1 right parenthesis end fraction blank$ is equal to

$stack lim with n rightwards arrow infinity below invisible function application not stretchy sum from r equals 1 to n of fraction numerator r over denominator 1 cross times 3 cross times 5 cross times 7 cross times 9 cross times midline horizontal ellipsis cross times left parenthesis 2 r plus 1 right parenthesis end fraction blank$ is equal to

If in a progression $a subscript 1 end subscript comma a subscript 2 end subscript comma horizontal ellipsis comma$ etc., $left parenthesis a subscript r end subscript minus a subscript r plus 1 end subscript right parenthesis$ bears a constant ratio with $a subscript r end subscript cross times a subscript r plus 1 end subscript$ , then the terms of the progression are in

If in a progression $a subscript 1 end subscript comma a subscript 2 end subscript comma horizontal ellipsis comma$ etc., $left parenthesis a subscript r end subscript minus a subscript r plus 1 end subscript right parenthesis$ bears a constant ratio with $a subscript r end subscript cross times a subscript r plus 1 end subscript$ , then the terms of the progression are in

If $a comma blank b$ , and $c$ are in G.P., then $a plus b comma blank 2 b$ , and $b plus c$ are in

If $a comma blank b$ , and $c$ are in G.P., then $a plus b comma blank 2 b$ , and $b plus c$ are in

parallel

If $a comma blank b comma$ and $c$ are in G.P., then the equations $a x to the power of 2 end exponent plus 2 b x plus c equals 0$ and $d x to the power of 2 end exponent plus 2 e x plus f equals 0$ have a common root if $fraction numerator d over denominator a end fraction comma fraction numerator e over denominator b end fraction comma fraction numerator f over denominator c end fraction$ are in

If $a comma blank b comma$ and $c$ are in G.P., then the equations $a x to the power of 2 end exponent plus 2 b x plus c equals 0$ and $d x to the power of 2 end exponent plus 2 e x plus f equals 0$ have a common root if $fraction numerator d over denominator a end fraction comma fraction numerator e over denominator b end fraction comma fraction numerator f over denominator c end fraction$ are in

Coefficients of $x to the power of 18 end exponent$ in $open parentheses 1 plus x plus 2 x to the power of 2 end exponent plus 3 x to the power of 3 end exponent plus horizontal ellipsis plus 18 x to the power of 18 end exponent close parentheses to the power of 2 end exponent$ is equal to

Coefficients of $x to the power of 18 end exponent$ in $open parentheses 1 plus x plus 2 x to the power of 2 end exponent plus 3 x to the power of 3 end exponent plus horizontal ellipsis plus 18 x to the power of 18 end exponent close parentheses to the power of 2 end exponent$ is equal to

If $a comma blank b comma$ and $c$ are in A.P., $p comma q$ and $r$ are in H.P. and $a p comma blank b q$ , and $c r$ are in G.P., then $fraction numerator p over denominator r end fraction plus fraction numerator r over denominator p end fraction$ is equal to

If $a comma blank b comma$ and $c$ are in A.P., $p comma q$ and $r$ are in H.P. and $a p comma blank b q$ , and $c r$ are in G.P., then $fraction numerator p over denominator r end fraction plus fraction numerator r over denominator p end fraction$ is equal to

parallel

If the sum of $m$ terms of an A.P. is the same as the sum of its $n$ terms, then the sum of its $left parenthesis m plus n right parenthesis$ terms is

If the sum of $m$ terms of an A.P. is the same as the sum of its $n$ terms, then the sum of its $left parenthesis m plus n right parenthesis$ terms is

The sum of 20 terms of a series of which every even term is 2 times the term before it, and every odd term is 3 times the term before it, the first term being unity is

The sum of 20 terms of a series of which every even term is 2 times the term before it, and every odd term is 3 times the term before it, the first term being unity is

The sum of the series $a minus open parentheses a plus d close parentheses plus open parentheses a plus 2 d close parentheses minus open parentheses a plus 3 d close parentheses plus horizontal ellipsis$ up to $left parenthesis 2 n plus 1 right parenthesis$ terms is

The sum of the series $a minus open parentheses a plus d close parentheses plus open parentheses a plus 2 d close parentheses minus open parentheses a plus 3 d close parentheses plus horizontal ellipsis$ up to $left parenthesis 2 n plus 1 right parenthesis$ terms is

parallel

If three positive real numbers $a comma blank b comma blank c$ are in A.P., such that $a b c equals 4$ , then the minimum value of $b$ is

If three positive real numbers $a comma blank b comma blank c$ are in A.P., such that $a b c equals 4$ , then the minimum value of $b$ is

In an A.P. of which $a$ is the first term, if the sum of the first $p$ terms is zero, then the sum of the next $q$ terms is

In an A.P. of which $a$ is the first term, if the sum of the first $p$ terms is zero, then the sum of the next $q$ terms is

If $x comma blank y comma$ and $z$ are $p to the power of t h end exponent comma blank q to the power of t h end exponent$ and $r to the power of t h end exponent$ terms respectively of an A.P. and also of a G.P., then $x to the power of y minus z end exponent y to the power of z minus x end exponent z to the power of x minus y end exponent$ is equal to

If $x comma blank y comma$ and $z$ are $p to the power of t h end exponent comma blank q to the power of t h end exponent$ and $r to the power of t h end exponent$ terms respectively of an A.P. and also of a G.P., then $x to the power of y minus z end exponent y to the power of z minus x end exponent z to the power of x minus y end exponent$ is equal to

parallel

If the sum of the first $2 n$ terms of the A.P. 2, 5, 8, …, is equal to the sum of the first $n$ terms of A.P. 57, 59, 61, …, then $n$ equals

If the sum of the first $2 n$ terms of the A.P. 2, 5, 8, …, is equal to the sum of the first $n$ terms of A.P. 57, 59, 61, …, then $n$ equals

If $a comma blank b comma$ and $c$ are in G.P. and $x comma blank y$ , respectively, be arithmetric means between $a comma blank b$ and $b comma blank c$ , then the value of $fraction numerator a over denominator x end fraction plus fraction numerator c over denominator y end fraction$ is

If $a comma blank b comma$ and $c$ are in G.P. and $x comma blank y$ , respectively, be arithmetric means between $a comma blank b$ and $b comma blank c$ , then the value of $fraction numerator a over denominator x end fraction plus fraction numerator c over denominator y end fraction$ is

The rational number which equals the number $Error converting from MathML to accessible text.$ with recurring decimal is

The rational number which equals the number $Error converting from MathML to accessible text.$ with recurring decimal is

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.