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

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

$- \frac{a (p + q) p}{q + 1}$
$\frac{a (p + q) p}{p + 1}$
$- \frac{a (p + q) q}{p - 1}$
None of these

The correct answer is: $negative fraction numerator a left parenthesis p plus q right parenthesis q over denominator p minus 1 end fraction$

Given, $S subscript p end subscript equals 0$ . Therefore,
$fraction numerator p over denominator 2 end fraction open square brackets 2 a plus open parentheses p minus 1 close parentheses d close square brackets equals 0 blank rightwards double arrow d equals fraction numerator negative 2 a over denominator p minus 1 end fraction$ (1)
Sum of next $q$ terms is sum of an A.P. whose first term will be
$T subscript p plus 1 end subscript equals a plus p d$
$therefore blank S equals fraction numerator q over denominator 2 end fraction left square bracket 2 open parentheses a plus p d close parentheses plus left parenthesis q minus 1 right parenthesis d right square bracket$
$equals fraction numerator q over denominator 2 end fraction left square bracket 2 a plus open parentheses p minus 1 close parentheses d plus left parenthesis p plus q right parenthesis d right square bracket$
$equals fraction numerator q over denominator 2 end fraction open square brackets 0 minus open parentheses p plus q close parentheses fraction numerator 2 a over denominator p minus 1 end fraction close square brackets$
$equals negative a fraction numerator left parenthesis p plus q right parenthesis q over denominator p minus 1 end fraction$ [Using (1)]

Related Questions to study

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

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

parallel

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

Let $left curly bracket t subscript n end subscript right curly bracket$ be a sequence of integers in G.P. in which $t subscript 4 end subscript colon t subscript 6 end subscript equals 1 colon 4$ and $t subscript 2 end subscript plus t subscript 5 end subscript equals 216$ . Then $t subscript 1 end subscript$ is

Let $left curly bracket t subscript n end subscript right curly bracket$ be a sequence of integers in G.P. in which $t subscript 4 end subscript colon t subscript 6 end subscript equals 1 colon 4$ and $t subscript 2 end subscript plus t subscript 5 end subscript equals 216$ . Then $t subscript 1 end subscript$ is

number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, and the last term exceeds the first by 10/2, then the number of terms in the series is

number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, and the last term exceeds the first by 10/2, then the number of terms in the series is

parallel

The largest term common to the sequences 1, 11, 21, 31, … to 100 terms and 31, 36, 41, … to 100 terms is

The largest term common to the sequences 1, 11, 21, 31, … to 100 terms and 31, 36, 41, … to 100 terms is

If the $p to the power of t h end exponent comma blank q to the power of t h end exponent$ , and $r to the power of t h end exponent$ terms of an A.P. are in G.P., then common ratio of the G.P. is

If the $p to the power of t h end exponent comma blank q to the power of t h end exponent$ , and $r to the power of t h end exponent$ terms of an A.P. are in G.P., then common ratio of the G.P. is

If $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divisible by $a x to the power of 2 end exponent plus c$ , then $a comma blank b comma blank c comma d$ are in

If $a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d$ is divisible by $a x to the power of 2 end exponent plus c$ , then $a comma blank b comma blank c comma d$ are in

parallel

If $alpha ϵ open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ , then $square root of x to the power of 2 end exponent plus x end root plus fraction numerator tan to the power of 2 end exponent invisible function application alpha over denominator square root of x to the power of 2 end exponent plus x end root end fraction$ is always greater than or equal to

If $alpha ϵ open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ , then $square root of x to the power of 2 end exponent plus x end root plus fraction numerator tan to the power of 2 end exponent invisible function application alpha over denominator square root of x to the power of 2 end exponent plus x end root end fraction$ is always greater than or equal to

The number of terms common between the series $1 plus 2 plus 4 plus 8 plus horizontal ellipsis$ to 100 terms and $1 plus 4 plus 7 plus 10 plus horizontal ellipsis$ to 100 terms is

The number of terms common between the series $1 plus 2 plus 4 plus 8 plus horizontal ellipsis$ to 100 terms and $1 plus 4 plus 7 plus 10 plus horizontal ellipsis$ to 100 terms is

Let $a equals 111 horizontal ellipsis 1$ (55 digits), $b equals 1 plus 10 plus 10 to the power of 2 end exponent plus horizontal ellipsis plus 10 to the power of 4 end exponent comma blank c equals 1 plus 10 to the power of 5 end exponent plus 10 to the power of 10 end exponent plus 10 to the power of 15 end exponent plus horizontal ellipsis plus 10 to the power of 50 end exponent$ , then

Let $a equals 111 horizontal ellipsis 1$ (55 digits), $b equals 1 plus 10 plus 10 to the power of 2 end exponent plus horizontal ellipsis plus 10 to the power of 4 end exponent comma blank c equals 1 plus 10 to the power of 5 end exponent plus 10 to the power of 10 end exponent plus 10 to the power of 15 end exponent plus horizontal ellipsis plus 10 to the power of 50 end exponent$ , then

parallel

Let $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript comma a subscript 4 end subscript$ and $a subscript 5 end subscript$ be such that $a subscript 1 end subscript comma a subscript 2 end subscript$ and $a subscript 3 end subscript$ are in A.P., $a subscript 2 end subscript comma a subscript 3 end subscript$ and $a subscript 4 end subscript$ are in G.P., and $a subscript 3 end subscript comma a subscript 4 end subscript$ and $a subscript 5 end subscript$ are in H.P. Then $log subscript e end subscript invisible function application a subscript 1 end subscript comma log subscript e end subscript invisible function application a subscript 3 end subscript$ and $log subscript e end subscript invisible function application a subscript 5 end subscript$ are in

Let $a subscript 1 end subscript comma a subscript 2 end subscript comma a subscript 3 end subscript comma a subscript 4 end subscript$ and $a subscript 5 end subscript$ be such that $a subscript 1 end subscript comma a subscript 2 end subscript$ and $a subscript 3 end subscript$ are in A.P., $a subscript 2 end subscript comma a subscript 3 end subscript$ and $a subscript 4 end subscript$ are in G.P., and $a subscript 3 end subscript comma a subscript 4 end subscript$ and $a subscript 5 end subscript$ are in H.P. Then $log subscript e end subscript invisible function application a subscript 1 end subscript comma log subscript e end subscript invisible function application a subscript 3 end subscript$ and $log subscript e end subscript invisible function application a subscript 5 end subscript$ are in

The $15 to the power of t h end exponent$ term of the series $2 fraction numerator 1 over denominator 2 end fraction plus 1 fraction numerator 7 over denominator 13 end fraction plus 1 fraction numerator 1 over denominator 9 end fraction plus fraction numerator 20 over denominator 23 end fraction plus horizontal ellipsis$ is

The $15 to the power of t h end exponent$ term of the series $2 fraction numerator 1 over denominator 2 end fraction plus 1 fraction numerator 7 over denominator 13 end fraction plus 1 fraction numerator 1 over denominator 9 end fraction plus fraction numerator 20 over denominator 23 end fraction plus horizontal ellipsis$ is

If $log subscript 2 end subscript invisible function application open parentheses 5 cross times 2 to the power of x end exponent plus 1 close parentheses comma log subscript 4 end subscript invisible function application left parenthesis 2 to the power of 1 minus x end exponent plus 1 right parenthesis$ and 1 are in A.P., then $x$ equals

If $log subscript 2 end subscript invisible function application open parentheses 5 cross times 2 to the power of x end exponent plus 1 close parentheses comma log subscript 4 end subscript invisible function application left parenthesis 2 to the power of 1 minus x end exponent plus 1 right parenthesis$ and 1 are in A.P., then $x$ equals

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.