Question

Bună! Mă puteți ajuta vă rog cu rezolvare?

1. 5+10+15+...+405
2. 25+26+...+50
3. 1+3+5+7+...+49

Mulțumesc anticipat! Zi frumoasă! ​

Answer 1

 

$\displaystyle\bf\\La~fiecare~exercitiu~alculam~mai~intai~numarul~de~termani~ (n).\\\\\\1)\\5+10+15+...+405=?\\\\n=\frac{405-5}{5}+1=\frac{400}{5}+1=80+1=81~de~termeni\\\\5+10+15+...+405=\frac{n(405+5)}{2}=\frac{81\times410}{2}=81\times205=\boxed{\bf16605}\\\\2)\\25+26+...+50=?\\\\n=\frac{50-25}{1}+1=25+1=26~de~termeni\\\\25+26+...+50=\frac{n(50+25)}{2}=\frac{26\times75}{2}= 13\times75=\boxed{\bf975}$

.

$\displaystyle\bf\\3)\\1+3+5+7+...+49=?\\\\n=\frac{49-1}{2}+1=\dfrac{48}{2}+1=24+1=25~de~termeni\\\\ 1+3+5+7+...+49=\frac{n(49+1)}{2}=\frac{25\times50}{2}=25\times25=\boxed{\bf25^2}=\boxed{\bf625}$