An arithmetic sequence has a first term of 10 and a sixth term of 40. what is the 20th term of this sequence?

124

Step-by-step explanation:

This is an arithmetic sequence

The nth term of an arithmetic sequence is Tn = a + (n-1)d

a is the first term.

n is the number of terms

d is the common difference

a is 10

The sixth term T6 = 10 + (6-1)d = 40

T6 = 10 - 5d = 40

5d = 40 - 10

5d = 30

d = 6

To get the 20th term T20

T20 = 10 + (20-1)6

T20 = 10 + 19(6)

T20 = 10 + 114

T20 = 124

a

step-by-step explanation:

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).