Answer:
a₁=1.5; d=7.
Step-by-step explanation:
1) according the condition S₁₋₉=117, it can be written as S₁₋₉=0.5*9*(a₁+a₉) or 0.5*9*(a₁+a₉)=117 - the first equation;
2) according to the condition S₁₀₋₁₃=91, it can be written as S₁₀₋₁₃=0.5*4*(a₁₀+a₁₃) or 0.5*4*(a₁₀+a₁₃)=91 - the second equation;
3) it is possible to make up the system of two equations:
[tex]\left \{ {{0.5*9*(a_1+a_9)=117} \atop {0.5*4*(a_{10}+a_{13})=91}} \right. \ => \ \left \{ {{a_1+a_9=26} \atop {a_{10}+a_{13}=\frac{91}{2}}} \right.[/tex]
4) if a₉=a₁+8d, a₁₀=a₁+9d and a₁₃=a₁+12d, then the system can be rewritten and solved:
[tex]\left \{ {{2a_1+8d=26} \atop {2a_1+21d=\frac{91}{2}}} \right. \ => \ \left \{ {{a_1=7} \atop {d=\frac{3}{2} }} \right.[/tex]
