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SAT Math 3.2 Algebra and Functions 178 Views


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SAT Math 3.2 Algebra and Functions

Language:
English Language

Transcript

00:02

And here's your shmoop du jour...

00:04

Each term in a sequence is one less than twice the previous term.

00:09

If the 5th term is 33, what is the first term?

00:14

Here are the potential answers...

00:18

So what do we know so far?

00:19

We know that in the sequence, the 5th term, n sub 5, is equal to 33,

00:25

and each subsequent term is one less than twice the previous...

00:29

...2 times the previous minus 1... is the equation.

00:32

However, we want to solve for the first term,

00:35

so instead of finding the next term, we want to go backwards.

00:40

We can solve the equation for n sub a, and then we'll be able to do that.

00:45

We add 1 to both sides, and then divide by 2.

00:49

We get that n sub a is equal to n sub a plus 1 plus 1 over 2.

00:55

So now, if we set n sub a plus 1 equal to 33, we can find the previous term, the fourth.

01:03

33 + 1 is 34; divide by 2 and we get 17.

01:08

So let's plug in 17 back into the equation, we get 17 + 1 = 18, over 2 which is 9.

01:16

This time, we plug in...9 + 1 which is 10, over 2 is 5.

01:21

Last one. 5 plus 1 is 6, over 2 is 3.

01:26

Finally, we get our answer.

01:28

The first term in our sequence is 3, so our answer is (B).

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