Question

a)22+25+28+...301
b)32+39+46+...753
Va roooog! Cat de repede!

Answer 1

$\displaystyle a).22+25+28+...+301 \\ \\ 301=22+(n-1) \cdot 3 \\ \\ 301=22+3n-3 \\ \\ 3n=301-22+3 \\ \\ 3n=282 \\ \\ n=94 \\ \\ S_{94}= \frac{2 \cdot 22+(94-1) \cdot 3}{2} \cdot 94 \\ \\ S_{94}=(44+93 \cdot 3) \cdot 47 \\ \\ S_{94}=(44+279) \cdot 47 \\ \\ S_{94}=323 \cdot 47 \\ \\ S_{94}=15181$

$\displaystyle b).32+39+46+...+753 \\ \\ 753=32+(n-1) \cdot 7 \\ \\ 753=32+7n-7 \\ \\ 7n=753-32+7 \\ \\ 7n=728 \\ \\ n=104 \\ \\ S_{104}= \frac{2 \cdot 32+(104-1) \cdot 7}{2} \cdot104 \\ \\ S_{104}=(64+103 \cdot 7) \cdot 52 \\ \\ S_{104}=(64+721) \cdot 52 \\ \\ S_{104}=785 \cdot 52\\ \\ S_{104}= 40820$