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In $\textit{sequences}$, it is important that we can; A $\textit{number sequence}$ is an ordered list of numbers defined by a rule. The numbers in the sequence are said to be its $\textit{terms}$. A sequence that continues forever is called an $\textit{infinite sequence}$. A sequence that terminates is called a $\textit{finite sequence}$. Example 1 Write down […]
Compound Interest is being used to calculate the total investment over time. Suppose John invests $1000 in the bank. He leaves the money in the bank for four years and is paid an interest rate of 10% per annum. The interest is added to his investment yearly, so the total value increases. The percentage increase […]
A geometric sequence is also referred to as a geometric progression. Each term of a geometric sequence can be obtained from the previous one by multiplying by the same non-zero constant. For example, \(2, \ 6, \ 18, \ 54, \cdots \) is a geometric sequence as each term can be obtained by multiplying the […]
An Arithmetic Sequence is a sequence in which each term differs from the previous one by the same fixed number. It can also be referred to as an arithmetic progression. For example, Algebraic Definition of Arithmetic Sequences If \( \{u_n\} \) is arithmetic, then \( u_{n+1} – u_n = d \)for all positive integers \( […]
Sequences may be defined in one of the following ways: listing all terms of a finite sequence:$2, 5, 8, 11, 14, 17$ listing the first few terms and assuming that the pattern represented continuous indefinitely:$2, 5, 8, \cdots $ giving a description in words:$\textit{Starts at 2, and each term is 3 more than the previous […]
A number Sequence or progression is an ordered list of numbers defined by a pattern or rule. The numbers in the sequence are said to be its numbers or terms. A sequence that continues indefinitely is called an infinite sequence. A sequence that ends is called a finite sequence. For example, \( 2, 5, 8, […]