internet intelligent tutors
In $\textit{sequences}$, it is important that we can; recognise a pattern in a set of numbers describe the pattern in words continue the pattern. A $\textit{number sequence}$ is an ordered list of numbers defined by a rule. The sequence starts at $4$ and add $5$ each time. $4, 9, 14, 19, \cdots$ The numbers in […]
Compound Interest is being used to calculate the total investment across over time. Suppose John invests $1000 in the bank. He leaves the money in the bank for 4 years, and are paid an interest rate of 10% per annum. The interest is added to his investment each year, so the total value increases. The […]
A geometric sequence is also referred to 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 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 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 Arithmetic Sequence If \( […]
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 […]
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 a finite sequence. For example, 2, 5, 8, 11, … […]