Question

PLEASE HELP ME WITH THIS PROBLEM!! THANK YOU!!

Answer 1

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 $a_n = 2*(a_{n-1}) - 3$

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}