The set of consist of the counting numbers, their opposite, and zero.
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Integers

Step-by-step explanation:

Counting Numbers are {1,2,3,4,5,...}

Its opposite would be -1,-2,-3,-4,-5,... respectively.

It includes 0 so the whole set would be

{ ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }

which is set of integers.

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step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.