Question Type 1: Finding the nth term given the first term and the common ratio Exercises

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

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

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

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

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

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

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

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

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

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

Calculate the 7th term of a geometric sequence with first term $u_1 = -3$ and ratio $r = -\tfrac12$.

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