1)An arithmetic series has common difference - 11 and tenth term 101. a) Find the first term of the series.
b )Find the sum of the first 30 terms of the series.

2) The fifth term of a geometric series is 12 and the eighth term of the series is 96
a) Find the common ratio
b) Find the first term of the series.
c) The sum of the first 20 terms, giving your answer to the nearest whole numbe

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step-by-step explanation:

8 2/3 is the answer

step-by-step explanation: just use a calculator

answer: 5100 just subtract

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