What do you call it when you add 1 2 3 etc.?

Question

Umm so i need to know what 1+2+3+4+5+6+7+8+9+10 all the way 150 is bleugh i know. I tried to write a formula for it but it didnt work :( my formula was 1 + 2 + 3 = 6 thats 3 numbers 1 + 2 + 3 +4 = 10 thats 4 numbers 1 + 2 + 3 +4 +5 = 15 so the difference between the 3 is +4, +5 the next would be +5 and so on. So i made the number of digits you want N so it would be N squared - N its self = the total

Where did i go wrong? because it doesn't work.

thanks!

I figured where i went wrong but umm yea what can i do and can you explain how to do it please :)

Theres a yr 13 or 11 way of doing it with coloums a b and c but i cant remeber quite how todo it
Amy

Answer 1

Let :



S= 1+2+3+...+ (N-2) + (N-1) + N



reverse it:



S= N+ (N-1) + (N-2) ... +3+2+1



Add by pairs:



2S = [1+N] + [2 + (N-1)] + [3+ (N-2)] + ... + [(N-1)+2] + [N+1]



2S = [N+1] +[N+1] + ... [N+1] .. (N times)



So: 2S = N(N+1)



Finally S = N(N+1)/2

Answer 2

Let's split your numbers into two lists:

1 + 2 + 3 + ... + 74 + 75



Now reverse the next numbers:

150 + 149 + 148 + ... + 77 + 76



Notice how, if you line them up this way, each pair of numbers adds up to 151:

(1 + 150 = 151)

(2 + 149 = 151)

(3 + 148 = 151)

etc.



You have 75 pairs x 151 = 11,325



P.S. The numbers in the sequence 1, 3, 6, 10, 15, 21 are called the "Triangle Numbers". That's because, if you draw rows of 1, 2, 3,etc. it forms a triangle with that many items.

*

**

***

**** <-- 4 rows = 10



The general formula is:

S(n) = n(n+1) /2



So...

(150 x 151)/2

= 11,325

Answer 3

Yea when you add a sequence it's called the sum of the first 150 terms, since it's an arithemtic progression (common difference between 2 terms is 1 , and the first term is represented by a1 = 1) to find the sum of the first 50 terms, you use this formula:



S150 (sum of first 150 terms) = n/2 [ 2(a1) + (n-1)d]

d is the common difference

n is 150 in this case



E-mail me for more details,



Good luck