Eric traveled to three cities on a single highway. The distance from the original location to the first city was 100 miles more than 5 times the distance from the first city to the second city. The distance from the second city to third was 10 miles less than 2 times the distance from the first city to the second city. If the distance from the original location to the first city and the distance from the second city to the third city were the same, what was the distance from the first city to the second city?

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

b. ol

step-by-step explanation:

i got the answer right on edg.

congruent: (geometry) (of figures) identical in form; coinciding exactly when superimposed.