The sea & sun souvenir shop is known for its specialty salt water taffy. every week, anthony fills a gigantic jar with taffy to put in the storefront display. this week, he puts in 500 pieces of cherry taffy but still has more space to fill. anthony fills the rest of the jar with banana taffy, his favorite flavor. in all, anthony puts 725 pieces of taffy in the jar. which equation can you use to find how many pieces of banana taffy b are in the jar?

you have to subtract the cherry taffy of 500 as that is not asked

725-500=225

b=725-500

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

i need points

step-by-step explanation: