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Now, let's work with a sequence, this sequence. We're going to find the first four
terms, and then the 10th and 15th terms
of the sequence with this formula which is called the "nth term."
All right, to find the first term, let n equal 1.
You can substitute 1
everywhere you see an "n" in in the formula.
Again the formula for a sequence is called the "nth term." Pronounced "enth term."
To find a second term
substitute 2 for every n.
Also notice that when -1 is raised to an even power
it becomes positive 1.
When -1 is raised to an odd power, it becomes or stays negative.
That accounts for the negative sign in front of
a term.
That's why the second term is -4,
because -1 was raised to the 5th power.
All right, to find the 3rd term,
let n equal 3. Substitute 3 for every n in the nth term
formula.
You'll have -1 to the 6th power (which will make it positive) times 9
So 9 is your answer; 9 is the 3rd term.
For the 4th term,
substitute 4 for every n.
You'll have -1 to the 4+3 power which is odd
and then 4-squared.
-1 to the seventh power equals -1.
So your final answer for the 4th term will be -16.
Now, to find the 10th term, let n equal 10.
Substitute 10 for every n in the nth term formula
You'll have -1 raised to an odd power
times 10-squared which is 100.
So your 10th term is -100.
Now to find the 15th term,
substitute 15 for every n in the nth term formula.
15 squared is 225
So you'll have -1 to an even power times 225.
So the 15th term will be positive 225.
This is called an alternating sequence,
and there are your answers.