# Sum of an Infinite Geometric Series

Home > Sequences and Series To examine the sum of all the terms of an infinite geometric sequence, we need to consider $S_n = \dfrac{u_1(1-r^n)}{1-r}$ when $n$ gets very large. Sum to Infinity If $\left|r\right|>1$, the series is said to be divergent and the sum infinitely large. For instance, when $r=2$ and $u_1=1$; $S_\infty=1+2+4+8+\cdots$ is [...]

# 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

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

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 | Math Help

Share0 Share +10 Tweet0 Our Courses A geometric sequence is also referred as a geometric progression. Each term of a geometric sequence can be obtained from the previous one my multiplying by the same non-zero constant. For example, $2, \ 6, \ 18, \ 54, \cdots$ is a geometric sequence as each term can […]

# Arithmetic Sequence | Maths Help

Share0 Share +10 Tweet0 An Arithmetic Sequence is a sequence in which each term differs from the previous one by the same fixed number. It cal also be referred to as an arithmetic progression. For example, 2, 5, 8, 11, … 10, 20, 30, 40, … 6, 4, 2, 0, 02, … Algebraic Definition of […]

# General Term of a Number Sequence

Share0 Share +10 Tweet0 The general term of a number sequence is one of many ways of defining sequences. Consider the tower of bricks. The first row has five bricks on top of the pile, the second row has six bricks, and the third row has seven bricks. If $T_n$ represents the number […]

# Understanding Number Sequence

Share0 Share +10 Tweet0 Number Sequence or progression is ordered list of numbers defined by a pattern or rule. The numbers in the sequence are said to be its numbers or its terms. A sequence which continues indefinitely is called an infinite sequence. A sequence which ends is called finite sequence. For example, 2, 5, […]

# Geometric Sequence using Logarithms

Share0 Share +10 Tweet0 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 $2, 4, 8, 16, \cdots$. Question 2 Find the smallest 5 digits term of the sequence \( […]

# 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 […]