Mathematics · Quantitative Aptitude

Number Sums and Series

268 Questions

Number sums and series questions test the ability to find patterns and calculate the sum of number sequences. These problems are a staple in the quantitative aptitude sections of various competitive exams. Practice this collection to improve speed and accuracy in solving arithmetic and geometric series problems.

Sum of consecutive integersGeometric series sumsRatio and proportion sumsOdd and even number propertiesRoman numeral calculations

Number Sums and Series Questions

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Express $49$ as the sum of $7$ odd numbers.
Express $121$ as the sum of $11$ odd numbers.

  1. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19$
  2. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19+21$
  3. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19+21$
  4. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$49=7^2=$ sum of first $7$ odd numbers.
So, $49=1+3+5+7+9+11+13$.
Similarly, $121=11^2=$ sum of first $11$ odd numbers. 
So, $121=1+3+5+7+9+11+13+15+19+21$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of:
$1+3+5+7+9+11+13+15+17+19+21+23$

  1. $11^2$
  2. $12^2$
  3. $10^2$
  4. $13^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$S _{n}=\dfrac{n}{2}\left [ 2a+(n-1)d \right ]$
$a =$ First term
$d =$ Common difference
$n =$ number of terms

Given series is an A.P.
with first term $=$ $1$
common difference $=$ $2$
and last term $=$ $23$

Sum $=$ $\dfrac{12}{2}$ $\times$ $(2+11\cdot 2)$ $=$ $12\times12$
Hence, Option B is correct.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

What is the series and also find the total of first $100$ consecutive odd numbers?

  1. $1 + 2 + 4 + 6 + 8 + 10 +... 100 = 12000$
  2. $2 + 3 + 4 + 7 + 9 + 11 +...100 = 10000$
  3. $1 + 3 + 5 + 7 + 10 + 11 +....100 = 1000$
  4. $1 + 3 + 5 + 7 + 9 + 11 +...100 = 10000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of first $100$ consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + ....+100 = 10000$
Since, we know the formula for sum of consecutive odd numbers $= n^2$
So, $n = 100$, Sum $= 100^2 = 10000$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of two consecutive number for $13^2$.

  1. $84$ and $85$
  2. $83$ and $84$
  3. $86$ and $82$
  4. $81$ and $80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$13^2= 169$
n = 13
$\dfrac{n^{2} - 1}{2} = \dfrac{13^{2} - 1}{2} = 84$
$\dfrac{n^{2} + 1}{2} = \dfrac{13^{2} + 1}{2} = 85$
So, the sum of two consecutive numbers = 84 + 85 = 169.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of two consecutive numbers for $15^2$.

  1. 112 and 113

  2. 113 and 114

  3. 115 and 112

  4. 113 and 115
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$15^2= 225$
n = 15
$\dfrac{n^{2} - 1}{2} = \dfrac{15^{2} - 1}{2} = 112$
$\dfrac{n^{2} + 1}{2} = \dfrac{15^{2} + 1}{2} = 113$
So, the sum of two consecutive numbers = 112 + 113 = 225.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

$96^{2}-1$ is a product of two consecutive odd numbers. Find those two odd numbers.

  1. 96 and 98

  2. 93 and 95

  3. 95 and 97

  4. 99 and 101
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$96^{2}-1 = 9215$
we can express the above number into general form $a^{2}-1 = (a + 1)\times (a - 1)$
Where a = 96
So, $96^{2}-1 = (96 + 1)\times (96 - 1)$
= $97 \times 95 = 9215$
Therefore, the two odd consecutive numbers are 95 and 97.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the series and also find the total of first 10 consecutive odd numbers.

  1. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
  2. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 16 + 17 + 19 = 101$
  3. $1 + 3 + 5 + 7 + 10 + 11 + 13 + 15 + 17 + 19 = 101$
  4. $1 + 3 + 6 + 6 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of first 10 consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
Since, we know the formula for sum of consecutive odd numbers = $n^2$
So, $n = 10$, Sum $= 10^2 = 100$