ACMMM071
establish and use the formula for the sum of the first \(n\) terms of an arithmetic sequence.
ACMMM071 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM068
recognise and use the recursive definition of an arithmetic sequence: \(t_{n+1}=t_n+d\)
ACMMM068 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM072
recognise and use the recursive definition of a geometric sequence:\(t_{n+1}=rt_n\)
ACMMM072 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM073
use the formula \(t_n=r^{n-1}t_1\) for the general term of a geometric sequence and recognise its exponential nature
ACMMM073 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM075
establish and use the formula \(S_n=t_1\frac{r^n-1}{r-1}\) for the sum of the first \(n\) terms of a geometric sequence
ACMMM075 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM069
use the formula \(t_n=t_1+\left(n-1\right)d\) for the general term of an arithmetic sequence and recognise its linear nature
ACMMM069 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM074
understand the limiting behaviour as \(n\rightarrow\infty\) of the terms \(t_n\) in a geometric sequence and its dependence on the value of the common ratio \(r\)
ACMMM074 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum