Harry ‘s painting class lasts for 5/6 of an hour each day. today he has been in class for 2/5 of an hour so far
how much more time is left in the class?

d, b, c, b

step-by-step explanation:

1. "find the first four terms of the sequence given by the formula dn = 3n (n − 1)."

n = 1: d₁ = 3(1) (1 − 1) = 3 (0) = 0

n = 2: d₂ = 3(2) (2 − 1) = 6 (1) = 6

n = 3: d₃ = 3(3) (3 − 1) = 9 (2) = 18

n = 4: d₄ = 3(4) (4 − 1) = 12 (3) = 36

2. "find the first four terms of the sequence given by the formula bn = 2n − 3."

n = 1: b₁ = 2(1) − 3 = 2 − 3 = -1

n = 2: b₂ = 2(2) − 3 = 4 − 3 = 1

n = 3: b₃ = 2(3) − 3 = 6 − 3 = 3

n = 4: b₄ = 2(4) − 3 = 8 − 3 = 5

3. "find an explicit formula that generates a sequence whose first four terms are 1000, 400, 160, 64."

first we need to identify if the sequence is arithmetic (has a common difference) or geometric (has a common ratio).

it's not arithmetic, because 400 − 1000 = -600 which is not the same as 160 − 400 = -240.

it is geometric, because 400 / 1000 = 160 / 400 = 64 / 160 = 0.4.

the first term is 1000, and the common ratio is 0.4, so:

sn = 1000 (0.4)^(n − 1)

or:

sn = 1000 (0.4)^n (0.4)^-1

sn = 2500 (0.4)^n

4. "find the simplest explicit formula that generates a sequence whose first terms are 2, 7, 12, 17."

this is an arithmetic sequence, because 7 − 2 = 12 − 7 = 17 − 12 = 5.

the first term is 2 and the common difference is 5, so:

sn = 2 + 5(n − 1)

however, this is not the simplest form of the equation.

sn = 2 + 5n − 5

sn = 5n − 3