Geometric Series

Geometric Series

Home > iitutor 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 geometric sequence, [...]
Arithmetic Series

Arithmetic Series

Home > iitutor 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 difference is [...]
Sigma Notation

Sigma Notation

Home > iitutor 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 on the [...]
Geometric Sequence Problems

Geometric Sequence Problems

Home > iitutor 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 chicken on [...]
Geometric Sequences

Geometric Sequences

Home > iitutor 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 to his [...]
Arithmetic Sequence Problems

Arithmetic Sequence Problems

Home > iitutor 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 and found [...]