The number of people that enter a contest the 1st day is 27. The 2nd day 31 people enter and 35 enter on the 3rd day. This pattern continues and the contest lasts 14 days.

What is the total number of people that enter the contest? Write the arithmetic series formula you used to determine the total number of people and show all the steps to find the solution

742

Step-by-step explanation:

27 + 31 + 35 + ...

a = 27

d = 31 - 27 = 4

S14 = (14/2)[2(27) + (14-1)(4)]

= 7(54 + 52)

= 7(106)

= 742

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