[tex]\displaystyle \bf\\
a_1;~a_4;~a_6 ~~~\text{\bf apartin unei progresii geometice cu ratia 2.}\\\\
a_4 = 2^3a_1 = 8a_1\\
a_6 = 2^5 a_1 = 32a_1\\\\
a_1+18;~~8a_1+34;~~32a_1+16~~~~\text{\bf sunt in progresie aritmetica.}\\\\
\frac{a_1+18 + 32a_1+16}{2} = 8a_1+34\\\\
\frac{33a_1+34}{2} = 8a_1+34\\\\
33a_1+34 = 2(8a_1+34)\\\\
33a_1+34 = 16a_1+68\\\\
33a_1 -16a_1 =68-34\\\\
17a_1=34\\\\
a_1 = \frac{34}{17} \\\\
\boxed{\bf a_1 =2}~si~\boxed{\bf q =2}
[/tex]