Question

Please help!!!

Please answer two of these questions and I’ll give 20 points!!

12. In a Fibonacci sequence, every term (except the first two) is the sum of the two
preceding terms. For example, 1, 1, 2, 3, 5, 8, 13, 21, ... is a Fibonacci sequence.
Find the sixteenth term of a Fibonacci sequence whose first two terms are -3 and 9.

13. If you buy 31 floops, the total cost will be less than 40$. But if you buy 32 floops, the total cost will be more than 41$. Assuming these prices do not involve tax, what is the cost of one floop?

Answer 1

12. If the first two terms of the sequence are -3 and 9, the next few terms are

-3 + 9 = 6

9 + 6 = 15

6 + 15 = 21

15 + 21 = 36

and so on. Continuing in this way, you'd find the 16th term to be 4359.

13. Let x be the cost of 1 floop.

31 floops cost less than $40, so 31x < 40 or x < 40/31.

32 floops cost more than $41, so 32x > 41 or x > 41/32.

Equivalently,

41/32 < x < 40/31

and

41/32 ≈ 1.28125

40/31 ≈ 1.29032

which means x = $1.29.