Answer: {2, 1, -1, -5}
I used spaces to make the answer more readable, though you won't type in any spaces because your teacher instructed this.
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Explanation:
The first term is 2 which is given to us.
Any terms after this are found by using the recursive function [tex]a_n = 2*(a_{n-1}) - 3[/tex]
I put parenthesis to show that the "n-1" is not part of the -3. This recursive function basically says "to get a new term, we double the last term, then subtract off 3"
In short the rule is "multiply by 2, then subtract 3"
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Since the first term is 2, this means,
second term = 2*(first term) - 3
second term = 2*(2) - 3
second term = 4-3
second term = 1
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Then we can say,
third term = 2*(second term) - 3
third term = 2*(1) - 3
third term = 2 - 3
third term = -1
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And finally,
fourth term = 2*(third term) - 3
fourth term = 2*(-1) - 3
fourth term = -2 - 3
fourth term = -5
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So in summary, we have
- first term = 2
- nth term = 2*(term just before the nth term) - 3
as the full recursive formula to generate the sequence {2, 1, -1, -5}
