[tex]a_2 + 7r = a_9 \\ - 3 + 7r = 46 \\ 7r = 49 | \div 7 \\ \boxed{ r = 7}[/tex]
[tex]a_1 + r = a_2 \\ a_1 + 7 = - 3 \\ \boxed{ a_1 = - 10}[/tex]
[tex]a_1 + 9r = a_{10} \\ - 10 + 9 \times 7 = a_{10} \\ - 10 + 63 = a_{10} \\ \boxed{a_{10} = 53}[/tex]
[tex]Sn = \frac{a_1 + a_n}{2} \times n[/tex]
[tex]S_{10}= \frac{ - 10 + a_{10}}{2} \times 10 \\S_{10}= \frac{ - 10 + 53}{2} \times 10 \\ S_{10}= \frac{43}{2} \times 10 \\ S_{10}= 21,5 \times 10 \\ \boxed{S_{10}= 215}[/tex]
