Use Gauss' formula: n(n+1)/2

sum of 1 through 27 = n(n+1)/2 = 27(28)/2= 27(14) = 378

but that's the sum of 1,2,3,...27

you want sum of 1,3,5,...27

subtract 2,4,6, ...26

they sum to twice 1,2,3, ...13 = n(n+1)/2 = 13(14)/2 =13(7) = 91

twice 91= 182

378-182 = 196

196 = 1+3+5 + ...27

Carl Gauss was a little boy in maybe 3rd grade or less. He was a precocious boy like Mozart writing music at a similarly young age. Gauss' math instructor got tired of Gauss and tried to give him something to take up his time for a while. He asked Gauss to add up all the numbers from 1 to 100. Gauss almost immediately said, based on n(n+1)/2 = 100(100+1)/2 = 50(101)= 5050

Gauss noticed that you could add 100+1 + 99+2 + 98+3 ... 50 times. 50 times 101 = 5050

he paired off the first and last numbers, 2nd and 2nd to last numbers, etc. 50 times & bingo 5050