Question

What is the explicit rule for the sequence?

Answer 1

This is an arithmetic sequence.
d= 0.5-3=-2.5
d= - 2.5
a(1)= 13
a(n) = a(1) +d(n-1)
a(n)=13-2.5(n-1)=13-2.5n+2.5= 15.5 - 2.5n
a(n)= 15.5 - 2.5n

Answer C. a(n)= 15.5 - 2.5n

Answer 2

`a_n=(1)/(2) (31-5n)=15.5-2.5n\\\\n\in N`

Explanation:

As you can see the sequence starts in 13 and it decreases 2.5 units every time, so, we can assume that the sequence starts at 15.5:

`a_1=15.5-2.5`

In this sense, we can infer that a possible sequence is:

`a_n=15.5-2.5n=(1)/(2) (31-5n)\\\\n\in N`

Let's verify it:

`a_1=15.5-2.5(1)=13\\a_2=15.5-2.5(2)=15.5-5=10.5\\a_3=15.5-2.5(3)=15.5-7.5=8\\a_4=15.5-2.5(4)=15.5-10=5.5\\a_5=15.5-2.5(5)=15.5-12.5=3\\a_6=15.5-2.5(6)=15.5-15=0.5`