Question

5+10+15+20+25+30+35+40+45+50+55+60+..............626

Answer 1

modul 1:
5+10+15+20+25+30+........................+625=(625+5)x(numarul de termeni):2
numarul de termeni=(625-5):5+1=620:5+1=124+1=125
(625+5)x125:2=630x62,5=39375
modul 2:
5+10+15+20+25+30+...........+625=5x125x(125+1):2=625x126:2=78750:2=39375

Answer 2

   
$\text{Consider ca ultimul termen este 625.} \\ \\ \text{Aflam numarul de termeni} \\ \\ n= \frac{625-5}{5}+1 = \frac{620}{5}+1 =124+1= 125\;de\;termeni. \\ \\ \\ 5+10+15+20+25+\hdots+625 = \\ \\ =\frac{125(625+5)}{2}= \frac{125\;\cdot\;630}{2}=125\;\cdot\;315 = \boxed{39375}$