Tag: arithmetic progression

Question 1

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The average of certain first consecutive even number is $101$. Find their sum?

$25,000$
$33,600$
$10100$
$24,960$

Reveal answer Fill a bubble to check yourself

Answer

$2^{4n-2}+(-1)^{n}2^{2n-1}$

Answer

$\sqrt{2}$

Answer

$\dfrac { \sqrt { a x } } { 1 + \sqrt { b } } + \dfrac { x } { 1 + \sqrt { y } }$

Answer

$\tan^{-1}\left(1\right)$

Question 2

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The sum of the series
$ _{ }^{ 4n }{ { C } _{ 0 } }+ _{ }^{ 4n }{ { C } _{ 4 } }+ _{ }^{ 4n }{ { C } _{ 8 } }+........ _{ }^{ 4n }{ { C } _{ 4n } }$ is

$2^{4n-2}+(-1)^{n+1}2^{2n-1}$
$2^{4n-2}-2^{2n-1}$
$2^{4n-2}+2^{2n-1}$

Reveal answer Fill a bubble to check yourself

Question 3

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The sum of the series $\overset { n }{ \underset { r=0 }{ \sum } } (r^2+1)(r!)$ is

$(n+1)!$
$(n+2)!-1$
$n(n+1)!$
$0$

Reveal answer Fill a bubble to check yourself

Question 4

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

$1+6+9(\dfrac{1^2 +2^2 +3^2}{7}) +12(\dfrac{1^2 +2^2 +3^2+4^2}{9} )+15(\dfrac{1^2 +2^2 +3^2+4^2+5^2}{11}) +$_____
Find sum of $15$ terms

$7720$
$7820$
$7980$
none of these

Reveal answer Fill a bubble to check yourself

Question 5

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

Find the sum of 1 + $\dfrac{1}{4} + \dfrac{1.3}{4.8} + \dfrac{1.3.5}{4.8.12} +.......\infty $

$2\sqrt{2}$
$\sqrt{2}$
$\sqrt { \frac { 1 }{ 2 } } $

Reveal answer Fill a bubble to check yourself

Question 6

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

Sum of values of $x ,$ which we should substitute in $( 1 )$ to give the sum of the series : $C _ { 0 } + C _ { 4 } + C _ { 8 } + C _ { 12 } + \ldots \ldots ,$ is -

$2$
$2 ( 1 + i )$
$2 ( 1 - i )$
$0$

Reveal answer Fill a bubble to check yourself

Question 7

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

If $0 < x , y , a , b < 1 ,$ then the sum of the infinite terms of the series
$\sqrt { x } ( \sqrt { a } + \sqrt { x } ) + \sqrt { x } ( \sqrt { a b } + \sqrt { x y } ) + \sqrt { x } ( b \sqrt { a } + y \sqrt { x } ) + \ldots$ is

$\dfrac { \sqrt { x } } { 1 + \sqrt { b } } + \dfrac { \sqrt { x } } { 1 + \sqrt { y } }$
$\dfrac { \sqrt { x } } { 1 - \sqrt { b } } + \dfrac { \sqrt { x } } { 1 - \sqrt { y } }$
$\dfrac { \sqrt { a x } } { 1 - \sqrt { b } } + \dfrac { x } { 1 - \sqrt { y } }$

Reveal answer Fill a bubble to check yourself

Question 8

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

If $S _ { n }$ denotes the sum of the terms in the $n ^ { t h }$ bracket of the series $( 1 ) + ( 3 + 5 ) + ( 7 + 9 + 11 ) + ( 13 + 15 + 17 + 19 ) + \ldots \ldots , \text { then } \left( S _ { 11 } - S _ { 9 } \right) =$

$362$
$432$
$602$
$632$

Reveal answer Fill a bubble to check yourself

Question 9

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The sum of the infinite terms of the series $\cot^{-1}\left(1^{2}+\dfrac{3}{4}\right)+\cot^{-1}\left(2^{2}+\dfrac{3}{4}\right)+\cot^{-1}\left(3^{2}+\dfrac{3}{4}\right)+..$ is equal to:

$\tan^{-1}\left(2\right)$
$\tan^{-1}\left(3\right)$
$\tan^{-1}\left(4\right)$

Reveal answer Fill a bubble to check yourself

Question 10

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

Sum infinite terms of the series $\cot ^ { - 1 } \left( 1 ^ { 2 } + \frac { 3 } { 4 } \right) + \cot ^ { - 1 } \left( 2 ^ { 2 } + \frac { 3 } { 4 } \right) + \cot ^ { - 1 } \left( 3 ^ { 2 } + \frac { 3 } { 4 } \right) + \ldots$ is

$\pi / 4$
$\tan ^ { - 1 } 2$
$\tan ^ { - 1 } 3$
$None\ of\ these$

Reveal answer Fill a bubble to check yourself

Tag: arithmetic progression

Questions Related to arithmetic progression