Find a30 of the arithmetic sequence:

−17,−7,3,13,...

a₃₀ = 273

Step-by-step explanation:

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 17 and d = a₂ - a₁ = - 7 - (- 17) = - 7 + 17 = 10 , then

a₃₀ = - 17 + (29 × 10) = - 17 + 290 = 273

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).