ShmoopTube

00:03

Here’s an unshmoopy question you’ll find on an exam somewhere in life…

00:07

The following table shows values for n and the corresponding values for a sub n.

00:12

Which of the following represents the relationship between n and a sub n?

00:18

And here are the potential answers...

00:22

OK, so this question is asking us to recognize a pattern…

00:27

…and if we glance at the answers, it’s one half times… something.

00:31

We can test each one.

00:35

So let’s start with A… input 0 for n and we get a-sub-n is zero.

00:41

So far so good.

00:42

If we input 1; well, when n is 1, a sub n is one half so A… doesn’t work.

00:48

Try B. when n is 0, a sub n is zero plus 1 here… times 1 half… which is 1 half…

00:57

so a sub n is one half. Doesn’t work.

01:00

Try C. when n is 0, a sub n is 0 – so far so good.

01:06

When n is 1, then 1 squared is 1 times ½, so – nope, C isn’t it either. We need the zero.

01:13

Try D. When n is zero, we are multiplying by a zero so yeah – zero works.

01:19

Try 1.

01:21

1 plus 1 is 2 times the quantity 1 times a half which gives us… 1.

01:28

Try 2. 2 plus 1 is 3 so we have one half times 2 times 3 which gives us 3 – yes!

01:36

We can check the others if we really need to, but none of our other choices worked and

01:40

this one seems golden, so… let’s pick D and move on with our lives.

01:43

D, as in… “Duck, duck… goose.”

Full Transcript