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 maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

If $T _n$ denotes the nth terms of the series.$ 2+3+6+11+18+..........$ , then $T _50$ is :

  1. $49^2-1$
  2. $49^2$
  3. $50^2+1$
  4. $49^2+2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$2+3+6+11+18+.................$

$\begin{matrix} { T _{ n } }=a{ x^{ 2 } }+bx+c \ { T _{ 1 } }=a+b+c=2 \ { T _{ 2 } }=a+b+c=3 \ { T _{ 3 } }=a+b+c=6 \ 3a+b=1 \ 5a+b=3 \ 2a=2 \ a=1 \ b=-2 \ c=3 \  \end{matrix}$
${T _n} = {n^2} - 2n + 3$
${T _{50}} = {\left( {50} \right)^2} - 2\left( {50} \right) + 3$
${T _{50}} = {\left( {49} \right)^2} + 2$
Hence,
Option $D$ is correct answer.

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

Find the next term of the series:
$22, 26, 29, 31,$ ..........

  1. $32$
  2. $33$
  3. $34$
  4. $35$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lets find the difference between the numbers of the series:

$22$       $26$       $29$       $31$       $x$.....
      $4$          $3$         $2$        $1$
Since, the difference is in A.P.
$\therefore x=31+1=32$
Hence, the answer is $32$.

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

Find the sum of the first $15$ terms of the following sequences having $n$th term as
${a} _{n}=3+4n$

  1. 525

  2. 563

  3. 184

  4. 189
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$a _{n}=3+4n$ (Given)

Now, 
$a _{1}=3+4\times 1=7$
$a _{2}=3+4\times 2=11$
$a _{3}=3+4\times 3=15$
So the series is
The sum of first is turns is
$S _{n}=\dfrac{n}{2}[2a+(n-1)d]$
$a=7, n=15, d=4$
$S _{n}=\dfrac{15}{2}[2\times 7+(15-1).4]$
$S _{n}=\dfrac{15}{2}[14+56]$
$S _{n}=\dfrac{15\times 70}{2}$
$S _{n}=15\times 35$
$S _{n}=525$
The sum of first $15$ terms of given series is 
$S _{n}=525$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

In each of the following questions, a series of number is given which follow certain rules. One of the number is missing. Choose the missing number from the alternatives given below and mark it on your answer-sheet as directed. $1, \dfrac {1}{3}, \dfrac {1}{9}, \dfrac {1}{27}, \dfrac {1}{81}, \dfrac {1}{243}, $?

  1. $\dfrac {1}{729}$
  2. $\dfrac {1}{829}$
  3. $\dfrac {1}{749}$
  4. $\dfrac {1}{769}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

G.P series with common ratio $\dfrac 13$

$\therefore$, next term is $\dfrac {1}{243} \times \dfrac {1}{3}=\dfrac {1}{729}$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

The number of terms in a sequence $6, 12, 24, ....1536$ represents a

  1. arithmetic progression

  2. harmonic progression

  3. geometric progression

  4. geometric series
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given series is $6,12,24,....1536$
Since, $\dfrac {12}{6} =2$ and $\dfrac {24}{12} =2$
i.e. the given sequence is a geometric sequence / progression. 
Multiple choice

What is the next term in the sequence 1, 4, 9, 16, ...?

  1. 21

  2. 25

  3. 28

  4. 36
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This sequence is the square of the natural numbers. The next term is the square of 5, which is 25.

Multiple choice

What is the 10th term in the Fibonacci sequence?

  1. 34

  2. 55

  3. 89

  4. 144
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers. The first two numbers in the sequence are 0 and 1. The next number is 0 + 1 = 1, the next number is 1 + 1 = 2, and so on. The 10th term in the Fibonacci sequence is 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 = 55.

Multiple choice

What is the missing number in the sequence: 1, 3, 5, ___, 9?

  1. 2

  2. 4

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sequence is increasing by 2, so the missing number is 7.

Multiple choice

What is the missing number in the sequence: 10, 8, 6, ___, 2?

  1. 3

  2. 4

  3. 5

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sequence is decreasing by 2, so the missing number is 4.

Multiple choice

The nth term of the sequence 2, 5, 8, .......is

  1. 3n + 2

  2. n2 + 1

  3. 3n - 1

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sequence is an arithmetic progression with first term a = 2 and common difference d = 3. The nth term is a + (n-1)d = 2 + (n-1)3 = 2 + 3n - 3 = 3n - 1.