Question

Nth term for the sequence: 30,27,24,21...

Answer 1

to find the nth term of a sequence use the formula:
Tn= a+(n-1)d
where a= first term d= common difference, Tn= nth term of the sequence
in this question a=30, d= -3
Tn= 30+(n-1)* -3
Tn= 30+-3(n-1)
Tn= 30-3n+3

Tn= -3n+33

Answer 2

`a_1=30;\ a_2=27;\ a_3=24;\ a_4=21;\ ...\\\\27=30-3\to a_2=a_1-3\\24=27-3\to a_3=a_2-3\\21=24-3\to a_4=a_3-3`


`this\ is\ an\ arithmetic\ sequence\\\\a_n=a_1+(n-1)d\leftarrow formula\ to\ nth\ term\ of\ arithmetic\ sequence\\\\a_1=30;\ d=a_2-a_1\to d=27-30=-3\\\\subtitute:\\\\a_n=30+(n-1)\cdot(-3)=30+(n)(-3)+(-1)(-3)=30-3n+3\\\\Answer:\boxed{a_n=-3n+33}`