Respuesta :
Answer:
Sequence 3
-10,-7.5,-5,-2.5,...
Step-by-step explanation:
So f(n+1)=f(n)+2.5 means a term can be found by adding it's previous term to 2.5. That means this is an arithmetic sequence with a common difference of 2.5.
f(n+1)=f(n)+d is the recursive form for an arithmetic sequence with common difference d.
So you are looking for a sequence of numbers that is going up by 2.5 each time.
Let's check sequence 1:
2.5+2.5=5 so not this one because we didn't get 6.25 next.
Let's check sequence 2:
2.5+2.5=5 is what we have for the 2nd term.
5+2.5=7.5 so not this one because we didn't get 10 next.
Let's check sequence 3:
-10+2.5=-7.5 is the 2nd term
-7.5+2.5=-5 is the 3rd term
-5+2.5=-2.5 is the 4th term
Sequence 3 is arithmetic with common difference 2.5 assuming the pattern continues.
Let's check sequence 4 for fun:
-10+2.5=-7.5 is not -25
So we are done. Sequence 3 is the only one that fits term=previous term+2.5 or f(n+1)=f(n)+2.5.
