a)
[tex]a_3=8\\a_4=16\\a_4=a_3*q\\16=8*q /:8\\2=q\\a_3=a_1*q^2\\8=a_1*2^2\\8=a_1*4\\2=a_1\\\\a_n=2*2^{n-1}[/tex]
b)
[tex]a_2=18\\a_5=\frac{16}3\\\\a_2=a_1*q\\18=a_1*q\\\frac{18}q=a_1\\\\a_5=a_1*q^4\\\frac{16}3=a_1*q^4\\\frac{16}3=\frac{18}q*q^4\\\frac{16}3=18*q^3 /:18\\\frac{16}3:18=q^3\\\frac{16}3*\frac1{18}=q^3\\q=\sqrt[3]{\frac{8}{27}}=\frac23\\\\a_1=18:\frac23=18*\frac32=9*3=27\\\\a_n=27*(\frac23)^n-1[/tex]
c)
[tex]a_2=\frac12\\a_7=-2\sqrt2\\a_2=a_1*q\\\frac12=a_1*q\\\frac{\frac12}{q}=a_1\\a_1=\frac12:q\\a_1=\frac12*\frac1q\\a_1=\frac1{2q}\\\\a_7=a_1*q^6\\-2\sqrt2=\frac1{2q}*q^6\\-2\sqrt2=\frac12q^5 /*2\\-4\sqrt2=q^5\\q=-\sqrt[5]{4\sqrt2}\\\\a_1=\frac{1}{2*(-\sqrt[5]{4\sqrt2})}=-\frac{\sqrt2}4\\\\a_n=-\frac{\sqrt2}4*(-\sqrt[5]{4\sqrt2})^{n-1}[/tex]
