SOLUTION: Use inductive reasoning to predict the next TWO numbers in the sequence. 80, –40, 20, –10, 5, . . . I can't figure out what the pattern is her necessarily. i get that its -

Algebra ->  Sequences-and-series -> SOLUTION: Use inductive reasoning to predict the next TWO numbers in the sequence. 80, –40, 20, –10, 5, . . . I can't figure out what the pattern is her necessarily. i get that its -      Log On


   

Question 133104This question is from textbook
: Use inductive reasoning to predict the next TWO numbers in the sequence.
80, –40, 20, –10, 5, . . .
I can't figure out what the pattern is her necessarily.
i get that its -120 +60 -30 +15 but i don't get what comes next.
Help me out with this please. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how each term is cut in half and is negated (ie the sign is changed). In other words, each term is multiplied by -1%2F2

Cut the 1st term 80 in half and negate it to get –40. In other words, %2880%29%28-1%2F2%29=-40

Cut the 2nd term –40 in half and negate it to get 20. In other words, %28-40%29%28-1%2F2%29=20

Cut the 3rd term 20 in half and negate it to get –10. In other words, %2820%29%28-1%2F2%29=-10

Cut the 4th term –10 in half and negate it to get 5. In other words, %28-10%29%28-1%2F2%29=5


So to find the next two terms, simply multiply the last few terms by -1%2F2


So lets multiply the last term 5 by -1%2F2

5%28-1%2F2%29=-5%2F2

So the next term is -5%2F2 or -2.5


Now lets multiply the last term -5%2F2 by -1%2F2

%28-5%2F2%29%28-1%2F2%29=5%2F4

So the next term is 5%2F4 or 1.25



So the updated sequence is

80, –40, 20, –10, 5, -5%2F2, 5%2F4