Question

What is the nth term rule of the linear sequence below?

27

,

25

,

23

,

21

,

19

,

Answer 1

The linear sequence 27,25,23,21,19,... is an arithmetic progression with a common difference of -2. For an arithmetic progression, the $n^{th}$ term is given as, $a_n=a_1+(n-1)d$  where $a_n$ is the $n^{th}$ term, $d=-2$ is the common difference and $a_1=27$ is the first term.

So, the $n^{th}$ term is given as, $a_n=27-2(n-1)=27-2n+2=29-2n$

Therefore the n$^{th}$ term rule is $a_n=29-2n$.