Geometric Series

Geometric Series

Home > Sequences and Series A $\textit{geometric series}$ is the sum of the terms of a geometric sequence. for example: $1, 2, 4, 8, \cdots , 2048$ is a finite geometric sequence. $1+2+4+8+ \cdots +2048$ is the corresponding finite geometric series. Geometric Series Formula If we are adding the first $n$ terms of an infinite [...]
Arithmetic Series

Arithmetic Series

Home > Sequences and Series An $\textit{arithmetic series}$ is the sum of the terms of an arithmetic sequence. For example: $4, 7, 10, 13, \cdots,61$ is a finite arithmetic sequence. $4+7+10+13+ \cdots +61$ is the corresponding arithmetic series. Arithmetic Series Sum of a Finite Arithmetic Series If the first term is $u_{1}$ and the common [...]
Sigma Notation

Sigma Notation

Home > Sequences and Series Another mathematical device that is widely used in sequences and series is called $\textit{sigma notation}$. The Greek letter, $\sum$ (capital sigma), is used to indicate the sum of a sequence. For example: $$\sum_{n=1}^{10}{n^2} = 1^2 + 2^2 + 3^2 + \cdots + 10^2$$ The limits of the sum, the numbers [...]
Geometric Sequence Problems

Geometric Sequence Problems

Home > Sequences and Series Growth and Decay Problems of growth and decay involve repeated multiplications by a constant number, common ratio. We can thus use geometric sequences to model these situations. $$\require{color} \color{red}u_{n} = u_{1} \times r^{n-1}$$ $$\require{color} \color{red}u_{n+1} = u_{1} \times r^{n}$$ Geometric Sequence Problems using Formula Example 1 The initial population of [...]
Geometric Sequences

Geometric Sequences

Home > Sequences and Series 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 $\textit{geometric progression}$. Geometric Sequences Formula David expects $10$% increase per month to deposit [...]
Arithmetic Sequence Problems

Arithmetic Sequence Problems

Home > Sequences and Series An arithmetic sequence is a sequence where there is a common difference between any two successive terms. $$\require{color} \color{red} u_{n} = u_{1}+(n-1)d$$ where $\require{color} \color{red} u_{1}$ is the first term and $\require{color} \color{red}d$ is the common difference of the arithmetic sequence. Arithmetic Sequence Problems Example 1 A city is studies [...]
Arithmetic Sequences

Arithmetic Sequences

Home > Sequences and Series Algebraic Definition An $\textit{Arithmetic Sequence}$ is a sequence in which each term differs from the previous one by the same fixed number, which is often called $\textit{common difference}$. It can also be referred to as an $\textit{arithmetic progression}$. A sequence in mathematics is an ordered set of numbers. An $\textit{arithmetic [...]
Geometric Series for Time Payments

Geometric Series for Time Payments

Share0 Share +10 Tweet0 Time payments is are calculated based on Geometric Series for reducible compound interests. Basically geometric series formula is used for handling this situation. Worked Examples of Geometric Series for Time Payments 1 John takes out a loan of $100 000 on 1st January 2001 for a home loan. Interest is charged […]