[latex]a_4-a_2=30[/latex] [latex]a_2+a_3=10[/latex] [latex]a_1q^{3}-a_1q=30[/latex] [latex]a_1q+a_1q^{2}=10[/latex] [latex]a_1(q^{3}-q)=30[/latex] [latex]a_1(q+q^{2})=10[/latex] (dzielimy stronami) [latex]frac{a_1(q^{3}-q)}{a_1(q+q^{2})}=3[/latex] [latex]frac{q^{3}-q}{q+q^{2}}=3 [/latex] [latex]frac{q(q^{2}-1)}{q(1+q)}=3[/latex] [latex]frac{q(q-1)(q+1)}{q(1+q)}=3 [/latex] [latex]frac{q(q-1)}{q}=3[/latex] [latex]q-1=3[/latex] [latex]q=4[/latex] [latex]a_1(q+q^{2})=10[/latex] [latex]a_1(4+16)=10[/latex] [latex]20a_1=10[/latex] [latex]a_1=frac{1}{2}[/latex] [latex]q=4[/latex] [latex]a_1=frac{1}{2}[/latex]
