Question

find 1+2+3+4....+80 the sum of the 80 natural numbers
the sum is ?

Answer 1

here is an old method reverse the order and sum the pairs

1 2 3 4 5 6 .... 79 80
+ 80 79 78 77 76 75... 2 1
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what does each pair add 2

Answer 2

i dont get it

Answer 3

ok... so what does each pair of numbers add to... of you add down each column

Answer 4

ok thanks

Answer 5

lol... why worry about learning.... when people just give answers... good luck

Answer 6

can u elavorate? i would like to learn too!

Answer 7

well each vertical pair adds to 81

does that make sense?

Answer 8

yes

Answer 9

and then?

Answer 10

well there are 80 pairs of numbers

and you have added the same number's twice...

so the sum is

Sum = 80 x 81/2

Answer 11

so in general, if you know the 1st and last number in an arithmetic sequence the sum is

\[S_{n} = \frac{n \times(a + l)}{2}\]

n = number of terms, a = 1st term and l = last term.

if you don't know the last term you need to use

\[S_{n} = \frac{n}{2} [ 2a + (n -1)\times d]\]

d is the common difference in the sequence... or what it is always changing by.

hope this make sense

Answer 12

yes thanks as well