Answer :
[tex]1+2+3+4+5+\dots+50\\\\1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\\where\ a_1=1\ and\ d=1\\\\Sum:S_n=\frac{a_1+a_n}{2}\cdot n\\\\S_{50}=\frac{1+50}{2}\cdot50=51\cdot25=1275\leftarrow solution[/tex]
Look at the first one and the last one: 1 + 50 = 51
Look at the second one and the second-last one: 2 + 49 = 51
Look at the third one and the third-last one: 3 + 48 = 51
Every pair you construct in this way adds up to 51 .
There are ( 50/2 ) = 25 pairs.
They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275
Look at the second one and the second-last one: 2 + 49 = 51
Look at the third one and the third-last one: 3 + 48 = 51
Every pair you construct in this way adds up to 51 .
There are ( 50/2 ) = 25 pairs.
They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275
