(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.