[tex]\displaystyle a).2+4+6+...+502 =2(1+2+3+...+251)= \\ \\ =2 \times \frac{251(251 +1)}{2} =2 \times \frac{251 \times 252}{2} \ \not 2 \times \frac{63252}{\not 2} =63252[/tex]
[tex]\displaystyle b). 5+8+11+...+902 \\ \\ 902=5+(n-1) \times 3 \\ \\ 902=5+3n-3 \\ \\ 3n=902-5+3 \\ \\ 3n=900 \\ \\ n= \frac{900}{3} \\ \\ n=300[/tex]
[tex]\displaystyle S_{300}= \frac{10+299 \times 3}{2} \times 300 \\ \\ S_{300}= \frac{10 +897}{2} \times 300 \\ \\ S_{300}= \frac{907}{2} \times 300 \\ \\ S_{300}=907 \times 150 \\ \\ S_{300}=136050[/tex]
