Question

How do you tell whether the sequence with the terms `a_2=0, a_3=-5, a_9=-35` is arithmetic?

Answer 1

Yes

Explanation:

Yes.
slope `=-5`

`T_n= -5n+b ; n=2 , 0 = -5*2+b or b= 10 :. T_n= -5n +10`

`T_n= -5n+10 ; T_9=-5*9+10= -35`

Alternative: Assuming it is arithmatic , common didifference

`d=a_3-a_2 = -5 ; a_1=a_2-d= 0-(-5)= 5 ; a_n=a_1+(n-1)d` or

`n=9 ; a_9 = 5+ (9-1)-5 = 5 -40 = -35`{verified)