Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 17: Mixed practice

Write down an explicit formula for the $n^{th}$ term of a geometric sequence $6, 3, 1.5, .....$

Find the ${10}^{th}$ term of a geometric sequence $6, 3, 1.5, .....$

A geometric sequence has common ratio $4$ and the $2^{nd}$ term is $9$ more than the $1^{st}$ term. Write down two different expressions for the second term in terms of $u_1$, the $1^{st}$ term.

A geometric sequence has common ratio $4$ and the $2^{nd}$ term is $9$ more than the $1^{st}$ term. Write an equation in $u_1$ and find the value of $u_1$.

A geometric sequence has common ratio $4$ and the $2^{nd}$ term is $9$ more than the $1^{st}$ term. Find the number of terms in the sequence that are less than $1000$.

A geometric sequence has first term $12$ and the third term $48$. The common ratio is $r$. Show that $r^2=4$.

A geometric sequence has first term $12$ and the third term $48$. The common ratio is $r$. Find the possible values for the common ratio.

A geometric sequence has first term $12$ and the third term $48$. The common ratio is $r$. Find the possible values of the $6^{th}$ term.