IB Mathematics Applications & Interpretation Question Type 1: Finding the Nth Term Given the First Term and the Common Ratio Exercises

An investment of $100 grows by 5% each year. Find its value after 20 years (compounded annually).

Find the 10th term of a geometric sequence with $u_1=7$ and $r=\frac{2}{3}$.

Find the 5th term of a geometric sequence where $u_1=5$ and $r=3$.

Write an expression for the $n$th term of a geometric sequence with first term $u_1=6$ and common ratio $r=0.5$.

A bacterial culture doubles every hour. If the initial population is 100, find the population after 10 hours.

Calculate the 4th term of a geometric sequence with $u_1=-2$ and $r=4$.

Find the 12th term of a geometric sequence with $u_1=3$ and $r=\frac{1}{3}$.

Write an expression for the $n$th term of a geometric sequence with first term $u_1=9$ and common ratio $r=-\frac{1}{3}$.

Find the 6th term of a geometric sequence with first term $u_1=3$ and common ratio $r=2$.

Calculate the 7th term of a geometric sequence with first term $u_1=-3$ and common ratio $r=-\frac{1}{2}$.

Determine the 5th term of a geometric sequence with $u_1=8$ and $r=-1.5$.

Find the 4th term of a geometric sequence where $u_1=2$ and $r=\sqrt{3}$.