Question

60+64+68.......+180
78+82+86.........+278

Answer 1

$\displaystyle a).60+64+68+...+180 \\ 180=60+(n-1) \times 4 \\ 180=60+4n-4 \\ 4n=180-60+4 \\ 4n=124 \\ n=124:4 \\ n=31 \\ S_{31}= \frac{120+30 \times 4}{2} \times 31 \\ \\ S_{31}= \frac{120+120}{2} \times 31 \\ \\ S_{31}= \frac{240}{2} \times 31 \\ \\ S_{31}=120 \times 31 \\ S_{31}=3720$
$\displaystyle b).78+82+86+...+278 \\ 278=78+(n-1) \times 4 \\ 278=78+4n-4 \\ 4n=278-78+4 \\ 4n=204 \\ n=204:4 \\ n=151 \\ S_{51}= \frac{156+50 \times 4}{2} \times 51 \\ \\ S_{51}= \frac{156+200}{2} \times 51 \\ \\ S_{51}= \frac{356}{2} \times 51 \\ \\ S_{51}=178 \times 51 \\ S_{51}= 9078$