Question

The 3rd and 6th term of a geometric progression are 9/2 and 243/16 respectively find the first term, common ratio, seventh term​

Answer 1

Hello,

Explanation:

`Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\(u_6)/(u_3) =r^3=((243)/(16) )/((9)/(2) ) =(27)/(8) =((3)/(2) )^3\\\\\boxed{r=(3)/(2) }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=(u_3)/(r^2) =((9)/(2) )/(((3)/(2^2)) ) =2\\\\\\u_7=u_6*(3)/(2) =(729)/(32)`