S1: Section 1 Algebra 151 equences
Question 3 of 7 | Pa
Question 3 (4 points)
Match the sequence (term) with the correct type of sequence (definition). (4 points)
Column A
Column B
1.
2,4,6,8,...
a. Geometric, common ratio is 2
2.
28, 24, 20, 16,...
b. Arithmetic common difference is 2
3.
2, 4, 8, 16,...
Geometric common ratio is 0.5
48, 24, 12.6
d. Arithmetic, common difference is -4

answer: c i think

step-by-step explanation:

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