Question

20+25+30+...............+90

Answer 1

5(4+5+6+...+45)=5*49*42=10290

unde 42=45-4+1, iar 49 rezulta din suma primului termen cu ultimul, al doilea cu penultimul etc. 

Answer 2

$\displaystyle 20+25+30+...+90 \\ \\ 90=20+(n-1) \times 5 \\ \\ 90=20+5n-5 \\ \\ 5n=90-20+5 \\ \\ 5n=75 \\ \\ n= \frac{75}{5} \\ \\ n=15$

$\displaystyle S_{15}= \frac{40+14 \times 5}{2} \times 15 \\ \\ S_{15}= \frac{40+70}{2} \times 15 \\ \\ S_{15}= \frac{110}{2} \times 15 \\ \\ S_{15}=55 \times 15 \\ \\ S_1_5=825$