Practice section 3 of 17

For each source-table list, state the first term $a$ and common ratio $r$: (a) $5,25,125,625$; (b) $27,9,3,1,1/3,1/9,1/27$; (c) $2,-6,18,-54,162$. Then decide whether (d) $2,4,6,10,14$ is a GP.

Write down the first term, common ratio and nth term of each GP: (i) $-1,2,-4,8,-16,\ldots$; (ii) $1,1/2,1/4,1/8,1/16,\ldots$.

A GP has first term $2$ and common ratio $8$. Find its seventh term. Find also the least positive integer $n$ such that its nth term exceeds $1\,000\,000$.

Find the sixth and thirteenth terms of a GP with first term $a=10$ and common ratio $r=\tfrac23$.

The third term of a GP is $36$ and its sixth term is $\tfrac{243}{2}$. Find its first term and common ratio.

Suppose $x,y,z$ are three consecutive terms of a GP with common ratio $r$. Write an equation relating $x,y,z$.