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class="entry single post-344 post type-post status-publish format-standard has-post-thumbnail hentry category-number-system category-quantitative-aptitude tag-sum tag-sum-of-natural-numbers tag-sum-of-numbers tag-sum-of-odd-numbers grow-content-body">
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Sum of n Consecutive numbers Like Natural, Even, Odd, Squares, Cubes


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Formulas with examples for Sum of n Consecutive numbers

In this page provide formulas with examples for sum of n consecutive natural numbers, sum of positive integers,  sum of n odd and even numbers, sum of consecutive squares of natural, odd, even numbers, sum of consecutive cube of natural, odd, even numbers.

Sum of natural, odd & even numbers

Sum of “n” natural numbers =  \frac{n(n+1)}{2}

Sum of “n” natural even numbers = (n ) (n + 1)

Sum of “n” natural odd numbers = n 2

Sum of square of natural, odd & even numbers

Sum of square of “n” first or consecutive square natural numbers:

Sum of square of "n" first or consecutive square natural numbers | Sum of n Consecutive numbers

Sum of square of “n” first or consecutive odd numbers:

Sum of square of "n" first or consecutive odd numbers | Sum of n Consecutive numbersSum of square of “n” first or consecutive square even numbers:

Sum of square of "n" first or consecutive square even number | Sum of n Consecutive numbers

Sum of cube natural, odd & even numbers

Sum of cube of first or consecutive ” n” natural numbers:

Sum of square of "n" first or consecutive square even number | Sum of n Consecutive numbers

 Sum of cube of first or consecutive ” n” even natural numbers = 2n2 (n + 1)2
Sum of cube of first or consecutive ” n” odd natural numbers = n2 (2n2 – 1)

Examples on sum of numbers

Ex . 1 : Find the sum of the first 50 positive integers.

Sol:   1 + 2 + 3+ 4+ 5+ ———-+50 So Here n = 50

= 50 ( 50+1) / 2 = 25 x 51 = 1275

Ex . 2 : Find the sum of the  consecutive numbers 25+26+27+28+ —–+100 .

Sol: 25+26+27+28+ —–+50 = ( 1+2+3+4+———+100) – (1+2+3+4+——-24)

= [ 100 ( 100+1) / 2 ] – [ 24 ( 24+1) / 2 ]

= 5050 – 300 = 4750.

Ex . 3 : Find the sum of the squares of the first 60 natural numbers.

Sol: 12 + 22 + 32 + 42+ 52 + ———-+602  So Here n = 60

= { 60 x (60 + 1) x [( 2 x 60 )+1 ] } / 6

= 60 x 61 x 121 / 6

=73810

Ex . 4 : what is the sum of first 100 odd numbers?

Sol : first 100 odd numbers means  1 + 3 + 5 +7 + ———-+ 199 so here n = 100

= 1002 = 10000

Ex . 5 : Find the sum of consecutive odd numbers  51 +53 +55 + ———+ 199.

Sol : 51 +53 +55 + ———+ 199 = {1 + 2+ 3  ———+ 199} – { 1 +2 + 3 + ———+ 49}

=1002  – 25

= 10000- 625 = 9375 .

Ex . 6 : Find the sum of the cubes of the first 25 positive integers.

Sol: 13 + 23+ 33+ 43+ 53 + ———-+253 So Here n = 25

= 252 x (25 +1 )2 / 4

= 625 x 676 / 4 = 105625

Ex . 6 : Find the sum of the cubes of the first 25 odd numbers.

Sol: First 25 odd cube numbers means 13 + 33+ 53 + ———-+493 So Here n = 25

= 25 2 [ (2 x  252 )– 1 ]

= 625 x [ 1250 – 1]

=625 x 1249 = 780625

Ex . 7 : Find the sum of the  consecutive cube numbers 263+283+ 303 + 323—–+1003 .

Sol : 263+283+ 303 + 323—–+1003 = {23+43+ 63 + 83—–+1003 }  – {23+43+ 63 + 83—–+243}

=(2 x 502 )(50 + 1)–  (2 x 122 )(12 + 1)2

= [ 5000 x 2601] –  [ 288 x 169 ]

= 13005000 – 48672 = 12956328.

Ex . 8 : Find the sum of the  consecutive square odd numbers 752 + 772 + 792 + 812+ 832 + ———-+992 .

Sol : 752 + 772 + 792 + 812+ 832 + ———-+992  = {12 + 22 + 32+—–+992 } – { 12 + 22 + 32 + —–+732}

= [ ( 50 ) (4*50 2 – 1) / 3 ] – [ ( 37 ) (4*37 2 – 1) / 3 ]

= [ 50  x 9999 / 3 ] – [ 37 x 5475 / 3]

= 166650 – 67525 = 99125

Sum of n natural numbers | Sum of odd and even numbers | Sum of the Squares of First n Positive Integers | Sum of the Cubes of First n Positive Integers | Sum of n Consecutive numbers

Some related Topics in Quantitative aptitude

The Concepts of number system the mathematics

Divisibility Rules of numbers from 1 to 20 | Basic math education

Simple interest and Compound interest formulas with examples

Percentage formulas | percentage calculations with examples

Circle formulas in math | Area, Circumference, Sector, Chord, Arc of Circle

Types of Quadrilateral | Quadrilateral formula for area and perimeter

Types of Triangles With examples | Properties of Triangle

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number system,
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Quantitative Aptitude

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My self Sivaramakrishna Alluri. Thank you for watching my blog friend

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7 thoughts on “Sum of n Consecutive numbers Like Natural, Even, Odd, Squares, Cubes


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    Sai Venkatesh malakala

    (July 8, 2018 - 8:20 am)
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    Thanks a lot


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      sivaalluri

      (July 9, 2018 - 2:09 pm)
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      Thank you Mr.Sai Venkatesh malakala


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    Bharathi

    (April 9, 2019 - 2:06 am)
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    Thank you sir, please provide more short cut tricks for competitive exams


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      sivaalluri

      (April 20, 2019 - 3:15 pm)
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      Definitely we will upload one by one


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    Ravindra Nath Mahto

    (May 11, 2019 - 5:33 am)
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    Thank you so much sir…


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      sivaalluri

      (May 11, 2019 - 3:43 pm)
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      Thank you


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    Vijay

    (April 16, 2023 - 8:08 am)
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    Thanks for the short trick, need your help to solve below question.
    Sum of cubes of six consecutive numbers is 15471. Find the sum of cubes of odd numbers and square of even numbers.


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Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

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Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431


Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

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Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431


Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431


Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431

Warning: mysqli_query(): (HY000/1194): Table 'wp_mtoptions' is marked as crashed and should be repaired in /home/sivaalluri33/public_html/allmathtricks.com/wp-includes/class-wpdb.php on line 2431