Question

6+11+16+21+..............+506 dau coronita

Answer 1

6+11+16+21+....+506=
(5*1+1)+(5*2+1)+(5*3+1)+(5*4+1)+...+(5*101+1)=
5(1+2+3+4+...+101)+101*1=
5($\frac{101*102}{2}$)+101=
5(101*51)+101=505*51+101=25755+101=25856

Answer 2

$\displaystyle \\ 6+11+16+21+...+506 \\ \\ 506=6+(n-1) \times 5 \\ \\ 506=6+5n-5 \\ \\ 5n=506-6+5 \\ \\ 5n=505 \\ \\ n= \frac{505}{5} \\ \\ n=101$

$\displaystyle S_{101}= \frac{12 +100 \times 5}{2} \times 101 \\ \\ S_{101}= \frac{12+500}{2} \times 101 \\ \\ S_{101}= \frac{512}{2} \times 101 \\ \\ S_{101}=256 \times 101 \\ \\ S_{101}=25856$