What recursive formula applies to generate the following sequence where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48
The applicable recursive formula for this sequence is
f(n + 1) = –2 f(n)
When n=1, f(n) equals 3
Now when n = 2
f(2) = -2 (3) = -6
When n = 3
f(3) = -2 (-6) = 12, and this pattern continues.
The inequalities we have are: option A: x + 1.5y ≤ 20, option C: x + 3y ≤ 36, option D: x ≥ 0, option H: y ≥ 0. To clarify, let's assume x represents the number of pasta packages and y represents the jars of pasta sauce. Since negative quantities are not permissible, we have x ≥ 0 and y ≥ 0. According to the condition, he has $36, and can carry up to 20 pounds of food in his backpack. Pasta is priced at $1 for a 1-pound package, while pasta sauce costs $3 for a jar weighing 1.5 pounds. If he purchases 'x' packs of pasta and 'y' jars of sauce, the equations become: Total cost = 1x + 3y ≤ 36 dollars and Total weight = 1x + 1.5y ≤ 20 pounds. Therefore, we derive four inequalities: option A: x + 1.5y ≤ 20, option C: x + 3y ≤ 36, option D: x ≥ 0, option H: y ≥ 0.
