Question

Gauss approach to find the sum 4+10+16+22+...+70

Answer 1

Each term in the sum differs by 6, so that the $n$th term is determined by $4+6(n-1)$. The last term is 70, so there are

$4+6(n-1)=70\implies n=12$

terms in the sum. If

$S=4+10+\cdots+64+70$

then it's also true that

$S=70+64+\cdots+10+4$

and joining the sums gives us

$2S=(4+70)+(10+64)+\cdots+(64+10)+(70+4)$

$2S=12\cdot74$

$S=\dfrac{12\cdot74}2\implies\boxed{S=444}$