Question

1+4+7+…+97+100=
????

Answer 1

Răspuns: 1717

Explicație pas cu pas:

$\\Notez~S=1+4+7+...+97+100\\\\S=\frac{(a_{1}+a_{n})\cdot{n}}{2}\\a_{1}=1, a_{2}=4...a_{n}=100\\\\r=a_{2}-a_{1}=4-1=3\\a_{n}=a_{1}+r(n-1)=>n=\frac{a_{n}-a_{1}}{r} +1\\\\n=\frac{100-1}{3}+1=\frac{99}{3} +1=34\\S=\frac{(1+100)\cdot\not{{34}}}{\not{2}} =101\cdot{17}=1717$