Question 149402: how do you figure out the nth term of :
21,19,17,15...
please help!!! xxx
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Lets assume this sequence is an arithmetic sequence. The general form of the arithmetic sequence is
 where  is the nth term, d is the difference, and  is the first term
So lets find the difference between 2 terms (i.e. the difference between two terms)
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To find the difference, simply pick any term and subtract the previous term from that selected term
 Select the 2nd term (which is 19) and subtract the 1st term (which is 21) from it.
So we get a difference of 
Lets pick another pair of terms to verify:
 Select the 3rd term (which is 17) and subtract the 2nd term (which is 19) from it.
And again, we get a difference of
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Lets pick another pair of terms to verify:
 Select the 4th term (which is 15) and subtract the 3rd term (which is 17) from it.
And again, we get a difference of
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Since we've tested every consecutive pair of terms, we've verified that the sequence has a constant difference of . This means the sequence is arithmetic
Since the difference is  and the first term is  , this means the arithmetic sequence is
 where  starts at 
Check:
Notice if we plug in we get
 plug in
 Multiply
 Add
which is our first term
Notice if we plug in  we get
 plug in
 Multiply
 Add
which is our second term
Notice if we plug in  we get
 plug in
 Multiply
 Add
which is our third term
Notice if we plug in  we get
 plug in
 Multiply
 Add
which is our fourth term
Since each term corresponds to the terms of the given list, this verifies our sequence.
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Answer:
So the list of numbers 21,19,17,15... can be generated by the sequence
where starts at
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! how do you figure out the nth term of :
21,19,17,15...
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Line the numbers up with 1,2,3,4...
1----21
2----21-1*2
3----21-2*2
4----21-3*2
...
n....21-(n-1)2 = 21-(2n-2)=21-2n+2 = 23-2n
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The nth term is a(n) = 23-2n
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Cheers,
Stan H.
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