Quantitative Aptitude

Number Series

2,662 Questions
All First differences and arithmetic progressions 812 Successive multiplication or division 429 Step-wise calculations 349 Squares and cubes based 338 Separate alternate positions 241 Inter-term operations 144 Mixed-operation rules 138 Unconventional pattern solving 74 Fractional and decimal operations 60 Prime number based 54 Digit operations 23

Number Series Questions

Multiple choice

$n^{th}$ term of the series $1+\dfrac { 4 }{ 5 } +\dfrac { 7 }{ { 5 }^{ 2 } } +\dfrac { 10 }{ { 5 }^{ 3 } } +..........................$
  1. $\dfrac { 3n+1 }{ { 5 }^{ n-1 } } $
  2. $\dfrac { 3n-1 }{ { 5 }^{ n } } $
  3. $\dfrac { 3n-2 }{ { 5 }^{ n-1 } } $
  4. $\dfrac { 3n+2 }{ { 5 }^{ n-1 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The numerators form an arithmetic progression 1, 4, 7, 10... with nth term 3n-2. The denominators form a geometric progression 5^0, 5^1, 5^2... with nth term 5^(n-1). Combining these gives (3n-2) / 5^(n-1).

Multiple choice

The sum of the first n terms of the series ${ 1 }^{ 2 }+2.{ 2 }^{ 2 }+{ 3 }^{ 2 }+2.{ 4 }^{ 2 }+{ 5 }^{ 2 }+2.{ 6 }^{ 2 }+...$ is $\dfrac { n{ \left( n+1 \right) }^{ 2 } }{ 2 } $ when n is even. When n is odd the sum is
  1. $\dfrac { 3n\left( n+1 \right) }{ 2 } $
  2. $\dfrac { { n }^{ 2 }\left( n+1 \right) }{ 2 } $
  3. $\dfrac { { n\left( n+1 \right) }^{ 2 } }{ 4 } $
  4. ${ \left[ \dfrac { n\left( n+1 \right) }{ 2 } \right] }^{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

$8^{th}$ term of series $\displaystyle 2\sqrt{2}+\sqrt{2}+0+......$ will be
  1. $\displaystyle -5\sqrt{2}$
  2. $\displaystyle 5\sqrt{2}$
  3. $\displaystyle 10\sqrt{2}$
  4. $\displaystyle -10\sqrt{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is an arithmetic progression with first term a = 2*sqrt(2) and common difference d = -sqrt(2). The n-th term is a + (n-1)d. For n = 8, term = 2*sqrt(2) + 7*(-sqrt(2)) = -5*sqrt(2).

Multiple choice

The sum of $24$ terms of the following series $2+4+6.....$
  1. $100$
  2. $200$ 
  3. $600$ 
  4. $250$ 
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is an arithmetic progression where the first term a=2 and the common difference d=2. The sum of the first n terms is given by (n/2) * (2a + (n-1)d). For n=24, the sum is (24/2) * (2*2 + (24-1)*2) = 12 * (4 + 46) = 12 * 50 = 600.