Danny works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 45 strands of lights to decorate 1 bush and 4 trees. This
afternoon, he strung lights on 4 bushes and 5 trees, using a total of 70 strands. Assuming
that all bushes are decorated one way and all trees are decorated another, how many strands
did Danny use on each?
strands of lights and every tree with
Danny decorated every bush with
strands.

5 strands for the bushes and 10 for the trees. Hope it helps!

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt