A sum of odd integers

Algebra Level 1

Evaluate

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19.


The answer is 100.

View wiki
Arron Kau by Arron Kau

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

9 solutions

(1+19)+(3+17)+...+(9+11)=20x5=100

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Nice approach, realizing that the pairs of numbers taken from the end all add up to 20.

keke mana ni

Cicak Dinding - 7 years, 10 months ago

[(l+1)/2]^2 where 'l' is the last odd number in the sequence

Hari Kumar - 7 years, 10 months ago

1+3+5+7+9+11+13+15+17+19 =(1+19)+(3+17)+(5+15)+(7+13)+(9+11) =20+20+20+20+20 =100

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Girija Lenka
Aug 3, 2013

{20 x 10} = 200 as there are 10 numbers so the answer will be 200/2 = 100

0 Helpful 0 Interesting 0 Brilliant 0 Confused

great job

thirumeny santhoshsivan - 7 years, 10 months ago
Caio Gonçalves
Jul 31, 2013

As somas dos elementos das extremidades, ou seja, os elementos os quais os 5 primeiros números iniciais se relacionam, ambos correpsondem a uma soma de resultado igual a 20. Multiplicado 20 pelas cinco pares que podem ser feitos, encontramos o valor final de 100.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1+19=3+17=5+15=7+13=9+11=20 so 20*5=100

0 Helpful 0 Interesting 0 Brilliant 0 Confused

great bro

thirumeny santhoshsivan - 7 years, 10 months ago
Ellimrac Leee
Jul 30, 2013

Just add them all :)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Matheus Pinto
Jul 29, 2013

1+3+5+7+9+11+13+15+17+19=100

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Também poderia ser calculado utilizando a formula da Soma de uma PA

Sn = a11+an . n / 2

S10= (1 + 19) . 2 / 2 = 100

Thauan Vieira de Barcellos - 7 years, 10 months ago

Log in to reply

Sim, correto.

Matheus Pinto - 7 years, 10 months ago
Souperman Arcena
Jul 29, 2013

1st and 10th number total is 20 which is applicable to 2nd to 9th,3rd to 8th and so on so 20 x 5= 100

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Yan Jie Chong
Jul 28, 2013

9 + 13 = 22 22/2 = 11

(9 * 11) + 1 = 100

0 Helpful 0 Interesting 0 Brilliant 0 Confused

100

Djsrabon Srabon - 7 years, 10 months ago

any increment sequence starts with {a} and has a step {d} can be written as a , a+d , a+2d , a+3d , a+4d ,
for our sequence here to get the i-th element we follow {element (i)= 1 + (i-1) 2 } and its summation follow { S(i)= i 1+ ( ( i )* (i-1) / 2) * 2 ) } putting i =10 , S(10)=10 + 90 =100

Amr Eldfrawy - 7 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...