# Tag Archives: Geometric Sequence # Total Distance Travelled by a Ball Dropped Comes to Rest

A ball is dropped from a height of $16$ metres onto a timber floor and bounces. After each bounce, the maximum height reached by the ball is $80 \%$ of the previous maximum height. Thus, after it first hits the floor, it reaches a height of $12.8$ metres before […] # Geometric Sequence Problems

Problems of growth and decay involve repeated multiplications by a constant number, common ratio. We can thus use geometric sequences to model these situations. \begin{align} \displaystyle\require{color} \color{red}u_{n} &= u_{1} \times r^{n-1} \\\require{color} \color{red}u_{n+1} &= u_{1} \times r^{n}\end{align} Example 1 The initial population of chicken on a farm was $40$. The population increased by $5$% […] # Geometric Sequence and Geometric Mean

Geometric Sequence Definition Geometric Sequences are sequences where each term is obtained by multiplying the preceding term by a certain constant factor, which is often called $\textit{common ratio}$. A geometric sequence is also referred to as a $\textit{geometric progression}$. David expects $10$% increase per month to deposit to his account. A $10$% increase per month […] # Geometric Sequence using Logarithms

Applications of Geometric Sequence using Logarithms Geometric Sequence using Logarithms is being used for finding the number of terms of geometric sequences. Question 1 Find the largest 5 digit term of the sequence $2, 4, 8, 16, \cdots$. \( \begin{aligned} \displaystyle2 \times 2^{n-1} &\lt 100000 \\2^{n} &\lt 100000 \\n &\lt \log_{2}{100000} \\n &\lt […]