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In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...
SAT Math 3.2 Algebra and Functions 178 Views
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SAT Math 3.2 Algebra and Functions
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?
Full Transcript
- 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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