Consider the sequences given in the table below. Find the least number, n, such that the nth term of the geometric sequence is greater than the corresponding term in the arithmetic sequence.

Find the 100th and the nth term for each of the following sequences.
a. 1, 8, 15, 22, ...
b. 50, 90, 130, ...
c. 1, 4, 16, ...
d. 6, 6 to the 4th power, 6 to the 7th power, 6 to the 10th power, ...
e. 185 + 6 * 3 to the 33rd power, 185 + 7 * 3 to the 33rd power, 185 + 8 * 3 to the 33rd power, ...

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

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

is there a graph

step-by-step explanation: