Answer:
1. a
2. d
3. c
4. b
Step-by-step explanation:
You're matching the formulas up with the sequences. Start with one of the formulas ("rules") and see if it matches up with any of the given sequences, that's what I would do.
So first, a little explanation:
A recursive formula tells you how to find a term of a sequence using the value of the previous term. another way to think of it is finding the next term of a sequence using a particular term.
aₙ refers to the nth term in a sequence. this means the position, such as first, second, third, etc.
So a₁ means the first term, and aₙ₋₁ refers to the term aₙ (aₙ will be the term we are talking about)
I'll explain as we go along.
1. aₙ=3+aₙ₋₁ ; a₁=2
The second part means that the sequence begins with 2, but all four sequences start with 2, so this doesn't help you narrow anything down.
The first part tells you that each term is derived by adding 3 to the previous term. how do you figure this out?
aₙ is the term in a given position. let's take n=2, for example. everywhere where there was n, substitute 2.
a₂=3+a₍₂₋₁₎=3+a₁
We already know that a₁=2, so a₂=3+2=5
You can try a few more examples, but by this point, it should be clear that recursive formula 1 matches up with sequence a.
2. The rule says that each term is the opposite of the term before it. Again, you can substitute values of n to see this for yourself. But the only sequence that satisfies this condition is d.
3. This rule states that each term is given by 5 minus the previous term. Let's try to find a₂: a₂=5-a₁
a₁=2 for all of the sequences, so a₂=5-2=3
The only sequence with a₂=3 is c.
Again, you can try this with more values of n. and if the sequences didn't all happen to begin with the same number, you would just have to do a little more trial and error.
4. Of course, there is only one answer left. but let's try to work through the problem anyway.
for n=2
a₂=2-a₁=2-2=0
and this matches up with b. I think this formula is the most confusing out of the four, but with a little patience, you should be okay.
Hopefully this helped!
