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

Statement 1:If sum f $n$ terms of a series $2 n to the power of 2 end exponent plus 3 n plus 1 comma$ then series is an AP.
Statement 2:Sum of $n$ terms of an AP is always of the form $p n to the power of 2 end exponent plus q n.$

Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
Statement 1 is True, Statement 2 is False
Statement 1 is False, Statement 2 is True

The correct answer is: Statement 1 is False, Statement 2 is True

Sum of $n$ terms of AP is given by $S subscript n end subscript equals fraction numerator n over denominator 2 end fraction open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets$ .
Hence, sum of $n$ terms of an AP is always of the form $p n to the power of 2 end exponent plus q n$
Hence, option $left parenthesis d right parenthesis$ is correct.

Related Questions to study

Let $a comma blank b comma blank c$ be three positive real numbers which are in HP.
Statement 1: $fraction numerator a plus b over denominator 2 a minus b end fraction plus fraction numerator c plus b over denominator 2 c minus b end fraction greater or equal than 4.$
Statement 2:If $x greater than 0 comma$ then $x plus fraction numerator 1 over denominator x end fraction greater or equal than 4.$

Let $a comma blank b comma blank c$ be three positive real numbers which are in HP.
Statement 1: $fraction numerator a plus b over denominator 2 a minus b end fraction plus fraction numerator c plus b over denominator 2 c minus b end fraction greater or equal than 4.$
Statement 2:If $x greater than 0 comma$ then $x plus fraction numerator 1 over denominator x end fraction greater or equal than 4.$

Statement 1:If $x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 25 z to the power of 2 end exponent equals x y z open parentheses fraction numerator 15 over denominator x end fraction plus fraction numerator 5 over denominator y end fraction plus fraction numerator 3 over denominator z end fraction close parentheses$ , then $x comma blank y comma blank z$ are in H.P.
Statement 2:If $a subscript 1 end subscript superscript 2 end superscript plus a subscript 2 end subscript superscript 2 end superscript plus horizontal ellipsis plus a subscript n end subscript superscript 2 end superscript equals 0$ , then $a subscript 1 end subscript equals a subscript 2 end subscript equals a subscript 3 end subscript equals horizontal ellipsis a subscript n end subscript equals 0$

Statement 1:If $x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 25 z to the power of 2 end exponent equals x y z open parentheses fraction numerator 15 over denominator x end fraction plus fraction numerator 5 over denominator y end fraction plus fraction numerator 3 over denominator z end fraction close parentheses$ , then $x comma blank y comma blank z$ are in H.P.
Statement 2:If $a subscript 1 end subscript superscript 2 end superscript plus a subscript 2 end subscript superscript 2 end superscript plus horizontal ellipsis plus a subscript n end subscript superscript 2 end superscript equals 0$ , then $a subscript 1 end subscript equals a subscript 2 end subscript equals a subscript 3 end subscript equals horizontal ellipsis a subscript n end subscript equals 0$

The harmonic mean of the roots of the equation $open parentheses 5 plus square root of 2 close parentheses x to the power of 2 end exponent minus open parentheses 4 plus square root of 5 close parentheses x plus 8 plus 2 square root of 5 equals 0$ is

The harmonic mean of the roots of the equation $open parentheses 5 plus square root of 2 close parentheses x to the power of 2 end exponent minus open parentheses 4 plus square root of 5 close parentheses x plus 8 plus 2 square root of 5 equals 0$ is

parallel

The sum to 50 terms of the series $fraction numerator 3 over denominator 1 to the power of 2 end exponent end fraction plus fraction numerator 5 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end fraction plus fraction numerator 7 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent end fraction plus horizontal ellipsis$ is

The sum to 50 terms of the series $fraction numerator 3 over denominator 1 to the power of 2 end exponent end fraction plus fraction numerator 5 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent end fraction plus fraction numerator 7 over denominator 1 to the power of 2 end exponent plus 2 to the power of 2 end exponent plus 3 to the power of 2 end exponent end fraction plus horizontal ellipsis$ is

If $a comma blank x$ and $b$ are in A.P., $a comma blank y comma$ and $b$ are in G.P. and $a comma blank z comma blank b$ are in H.P. such that $x equals 9 z$ and $a greater than 0 comma blank b greater than 0$ , then

If $a comma blank x$ and $b$ are in A.P., $a comma blank y comma$ and $b$ are in G.P. and $a comma blank z comma blank b$ are in H.P. such that $x equals 9 z$ and $a greater than 0 comma blank b greater than 0$ , then

Let $a subscript 1 end subscript comma a subscript 2 end subscript comma horizontal ellipsis comma a subscript 10 end subscript$ be in A.P. and $h subscript 1 end subscript comma h subscript 2 end subscript comma horizontal ellipsis comma h subscript 10 end subscript$ be in H.P. If $a subscript 1 end subscript equals h subscript 1 end subscript equals 2$ and $a subscript 10 end subscript equals h subscript 10 end subscript equals 3$ , then $a subscript 4 end subscript h subscript 7 end subscript$ is

Let $a subscript 1 end subscript comma a subscript 2 end subscript comma horizontal ellipsis comma a subscript 10 end subscript$ be in A.P. and $h subscript 1 end subscript comma h subscript 2 end subscript comma horizontal ellipsis comma h subscript 10 end subscript$ be in H.P. If $a subscript 1 end subscript equals h subscript 1 end subscript equals 2$ and $a subscript 10 end subscript equals h subscript 10 end subscript equals 3$ , then $a subscript 4 end subscript h subscript 7 end subscript$ is

parallel

If $x comma blank y comma blank z$ are real and $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 16 z to the power of 2 end exponent minus 6 x y minus 12 y z minus 8 z x equals 0$ , then $x comma blank y comma blank z$ are in

If $x comma blank y comma blank z$ are real and $4 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent plus 16 z to the power of 2 end exponent minus 6 x y minus 12 y z minus 8 z x equals 0$ , then $x comma blank y comma blank z$ are in

Let $alpha comma blank beta element of R$ . If $alpha comma blank beta to the power of 2 end exponent$ be the roots of quadratic equation $x to the power of 2 end exponent minus p x plus 1 equals 0$ and $alpha to the power of 2 end exponent comma beta$ be the roots of quadratic equation $x to the power of 2 end exponent minus q x plus 8 equals 0$ , then the value of ‘ $r$ ’ if $fraction numerator r over denominator 8 end fraction$ be arithmetic mean of $p$ and $q$ is

Let $alpha comma blank beta element of R$ . If $alpha comma blank beta to the power of 2 end exponent$ be the roots of quadratic equation $x to the power of 2 end exponent minus p x plus 1 equals 0$ and $alpha to the power of 2 end exponent comma beta$ be the roots of quadratic equation $x to the power of 2 end exponent minus q x plus 8 equals 0$ , then the value of ‘ $r$ ’ if $fraction numerator r over denominator 8 end fraction$ be arithmetic mean of $p$ and $q$ is

If $a comma fraction numerator 1 over denominator b end fraction comma blank c$ and $fraction numerator 1 over denominator p end fraction comma blank q comma fraction numerator 1 over denominator r end fraction$ form two arithmetic progressions of the same common difference, then $a comma blank q comma c$ are in A.P. if

If $a comma fraction numerator 1 over denominator b end fraction comma blank c$ and $fraction numerator 1 over denominator p end fraction comma blank q comma fraction numerator 1 over denominator r end fraction$ form two arithmetic progressions of the same common difference, then $a comma blank q comma c$ are in A.P. if

parallel

If $open vertical bar a close vertical bar less than 1$ and $open vertical bar b close vertical bar less than 1$ , then the sum of the series $1 plus open parentheses 1 plus a close parentheses b plus open parentheses 1 plus a plus a to the power of 2 end exponent close parentheses b to the power of 2 end exponent plus open parentheses 1 plus a plus a to the power of 2 end exponent plus a to the power of 3 end exponent close parentheses b to the power of 3 end exponent plus horizontal ellipsis$ is

If $open vertical bar a close vertical bar less than 1$ and $open vertical bar b close vertical bar less than 1$ , then the sum of the series $1 plus open parentheses 1 plus a close parentheses b plus open parentheses 1 plus a plus a to the power of 2 end exponent close parentheses b to the power of 2 end exponent plus open parentheses 1 plus a plus a to the power of 2 end exponent plus a to the power of 3 end exponent close parentheses b to the power of 3 end exponent plus horizontal ellipsis$ is

The value of $not stretchy sum from r equals 0 to n of open parentheses a plus r plus a r close parentheses open parentheses negative a close parentheses to the power of r end exponent$ is equal to

The value of $not stretchy sum from r equals 0 to n of open parentheses a plus r plus a r close parentheses open parentheses negative a close parentheses to the power of r end exponent$ is equal to

The sum of series $1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$ is

The sum of series $1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$ is

parallel

If $t subscript n end subscript equals fraction numerator 1 over denominator 4 end fraction open parentheses n plus 2 close parentheses left parenthesis n plus 3 right parenthesis$ for $n equals 1 comma blank 2 comma blank 3 comma blank horizontal ellipsis comma blank$ then $fraction numerator 1 over denominator t subscript 1 end subscript end fraction plus fraction numerator 1 over denominator t subscript 2 end subscript end fraction plus fraction numerator 1 over denominator t subscript 3 end subscript end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator t subscript 2003 end subscript end fraction equals$

If $t subscript n end subscript equals fraction numerator 1 over denominator 4 end fraction open parentheses n plus 2 close parentheses left parenthesis n plus 3 right parenthesis$ for $n equals 1 comma blank 2 comma blank 3 comma blank horizontal ellipsis comma blank$ then $fraction numerator 1 over denominator t subscript 1 end subscript end fraction plus fraction numerator 1 over denominator t subscript 2 end subscript end fraction plus fraction numerator 1 over denominator t subscript 3 end subscript end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator t subscript 2003 end subscript end fraction equals$

The sum to 50 terms of the series $1 plus 2 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses plus 3 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses to the power of 2 end exponent plus horizontal ellipsis$ is given by

The sum to 50 terms of the series $1 plus 2 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses plus 3 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses to the power of 2 end exponent plus horizontal ellipsis$ is given by

The line $x plus y equals 1$ meets $x$ -axis at $A$ and $y$ -axis at $B comma blank P$ is the mid-point of $A B$ ;
$P subscript 1 end subscript$ is the foot of the perpendicular from $P$ to $O A$ :
$M subscript 1 end subscript$ is that of $P subscript 1 end subscript$ from $O P$ ; $P subscript 2 end subscript$ is that of $M subscript 1 end subscript$ from $O A$ ; $M subscript 2 end subscript$ is that of $P subscript 2 end subscript$ from $O P$ ; $P subscript 3 end subscript$ is that of $M subscript 2 end subscript$ from $O A$ ; and so on.
If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is

The line $x plus y equals 1$ meets $x$ -axis at $A$ and $y$ -axis at $B comma blank P$ is the mid-point of $A B$ ;
$P subscript 1 end subscript$ is the foot of the perpendicular from $P$ to $O A$ :
$M subscript 1 end subscript$ is that of $P subscript 1 end subscript$ from $O P$ ; $P subscript 2 end subscript$ is that of $M subscript 1 end subscript$ from $O A$ ; $M subscript 2 end subscript$ is that of $P subscript 2 end subscript$ from $O P$ ; $P subscript 3 end subscript$ is that of $M subscript 2 end subscript$ from $O A$ ; and so on.
If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is
Maths-General

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.