Tag: forming an arithmetic progression between two quantities a and b

Question 1

Find $(3^{3}-2^{3})+(5^{3}-4^{3})+(7^{3}-6^{3})+$ to $10$ terms.

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

$4,670$
$4,870$
$4,800$
$4,960$

Answer

Correct Option: A

Question 2

The sum of the series $\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{3.4}-..\infty$ is

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

$log _{e}2$
$2log _{e}2$
$log _{e}2-1$
$log _{e}\dfrac{4}{e}$

Answer

Correct Option: A

Question 3

Find the sum of The first $15$ multiples of $8$

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

The firs $40$ positive integers divisible by $(a)3(b)5(c)6.$
All $3-$ digit natural numbers which are divisible by $13$.
All $3-$ digit natural numbers, which area multiples of $11$.
All $2-$ digit natural numbers divisible by $4$.

Answer

Correct Option: A

Question 4

The sum of the series$\dfrac{1}{2!}+ \dfrac{1}{4!}+ \dfrac{1}{6!}+$ is

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

$\dfrac{e^{2}-1}{2}$
$\dfrac({e-1})^{2}{2e}$
$\dfrac{e^{2}-1}{2e}$
$\dfrac{e^{2}-2}{e}$

Answer

Correct Option: A

Question 5

The sum of $\frac{1}{3\sqrt{1}+1\sqrt{3}}+\frac{1}{5\sqrt{3}+3\sqrt{5}}+\frac{1}{7\sqrt{5}+5\sqrt{7}}+...+\frac{1}{225\sqrt{223}+223\sqrt{225}}$ is

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

$\frac{123}{125}$
$\frac{124}{125}$
$\frac{14}{15}$
$\frac{7}{15}$

Answer

Correct Option: A

Question 6

A sum to $n$ terms of the series $\dfrac{3}{2^1 \cdot 2 \cdot 1} + \dfrac{4}{2^2 \cdot 3 \cdot 2} + \dfrac{5}{2^3 \cdot 4 \cdot 3} + \dfrac{6}{2^4 \cdot 5 \cdot 4} + ...$ is $S _n$ then

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

$S _{10} = \dfrac{11263}{11264}$
$S _{10} = \dfrac{22527}{11264}$
If $n$ approaches $\infty, S _n$ approaches to $1$
If $n$ approaches $\infty, S _n$ approaches to $2$

Answer

Correct Option: A

Question 7

Sum to infinity of the $\dfrac{2}{3}$ - $\dfrac{5}{6}$ + $\dfrac{2}{3}$ - $\dfrac{11}{24}$+ ....... is

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

$\dfrac{4}{9}$
$\dfrac{1}{3}$
$\dfrac{2}{9}$
none of these

Answer

Correct Option: A

Question 8

what is the sum of $20.08, 20.008 , 20.088$ and $20.888 ?$

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

$81.064$
$81.604$
$80.064$
$80.888$

Answer

Correct Option: A

Question 9

The sum of digits of all numbers from 1 to 300 is equal to

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

3000
3003
3033
none of these

Answer

Correct Option: A

Question 10

the sum to infinity of the series
$1+\frac { 2 }{ 5 } +\frac { 6 }{ { 5 }^{ 2 } } +\frac { 10 }{ { 5 }^{ 3 } } +\frac { 14 }{ { 5 }^{ 4 } } +.....$ is

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

$\frac { 4 }{ 7 } $
$\frac { 5 }{ 4 } $
$\frac { 7 }{ 4 } $
$\frac { 6 }{ 5 } $

Answer

Correct Option: A

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