Question

Find the sum of 14+20+26+...+1244

Answer 1

If

`S=14+20+26+\cdots+1232+1238+1244`

then

`S=1244+1238+1232+\cdots+26+20+14`

We can pair terms in the same positions to get

`2S=(14+1244)+(20+1238)+\cdots+(1238+20)+(1244+14)`

`2S=\underbrace{1258}_{206\text{ times}}`

`\implies S=\frac{206\cdot1258}2=\boxed{129,574}`

We know there are 206 copies of 1258 being added because

`14+6(n-1)=1244\implies n=206`