IB Mathematics Analysis and Approaches Question Type 1: Finding the Nth Term Given First Term and Common Ratio Exercises

Find the sixth term of the geometric sequence with first term $3$ and common ratio $2$.

Express the $n$th term $u_n$ of the geometric sequence with first term $u_1=2b$ and common ratio $r=-3$ in terms of $b$ and $n$.

Express the $n$th term $u_n$ of the geometric sequence with first term $u_1=p$ and common ratio $r=\frac{2}{5}$ in terms of $p$ and $n$.

Find $u_7$ for the geometric sequence with first term $u_1=5$ and common ratio $r=\frac{1}{2}$. [2 marks]

Find $u_4$ for the geometric sequence with first term $u_1=9$ and common ratio $r=\sqrt{3}$. [2 marks]

Express the $n$th term $u_n$ of the geometric sequence with first term $u_1=a$ and common ratio $r=2$ in terms of $a$ and $n$.

Find $u_{10}$ for the geometric sequence with first term $u_1=7$ and common ratio $r=0.8$.

Find $u_6$ for the geometric sequence with first term $u_1=2$ and common ratio $r=-2$. [2 marks]

Find $u_4$ for the geometric sequence with first term $u_1=1.5$ and common ratio $r=4$.

Find $u_5$ for the geometric sequence with first term $u_1=12$ and common ratio $r=0$.

Find $u_5$ for the geometric sequence with first term $u_1=4$ and common ratio $r=\frac{2}{3}$.

Find $u_5$ for the geometric sequence with first term $u_1=-4$ and common ratio $r=3$.

Find $u_6$ for the geometric sequence with first term $u_1=3$ and common ratio $r=2$.

Find $u_9$ for the geometric sequence with first term $u_1=-3$ and common ratio $r=-\frac{1}{3}$.