[tex]a_2=\frac{3}{4}, \ a_5=\frac{3}{32}\\\\a_5=a_2\cdot q^3\\\\\frac{3}{4}\cdot q^3=\frac{3}{32} \ \ |\cdot\frac{4}{3}\\\\q^3=\frac{1}{8}\longrightarrow q=\frac{1}{2}\\\\a_5=a_1\cdot q^4\\\\a_1\cdot(\frac{1}{2})^4=\frac{3}{32}\\\\a_1\cdot\frac{1}{16}=\frac{3}{32} \ \ |\cdot16\\\\a_1=\frac{3}{2}=1,5\\\\S_n=a_1\cdot\frac{1-q^n}{1-q}\\\\S_4=1,5\cdot\frac{1-(\frac{1}{2})^4}{1-\frac{1}{2}}=1,5\cdot\frac{\frac{15}{16}}{\frac{1}{2}}=1,5\cdot(\frac{15}{16}\cdot2)=\\\\=1,5\cdot\frac{15}{8}=1,5\cdot1,875=2,8125[/tex]
Odp. a₁ = 1,5 ⇒ q = 0,5 ⇒ S₄ = 2,8125
