Mathematics - Sequence & Series Question with Solution | TestHub

Let $A_1,A_2,\dots ,A_m$ be arithmetic means between -2 and 1027, and $G_1,G_2,\dots ,G_n$ be geometric means between 1 and 1024. The product $G_1{G}_2\cdots G_n$ is $2^{45}$ and $A_1+\cdots +A_m=1025\times 171$. Find n.