Select the correct answer. What is the sum of this arithmetic series?

586 +564 + 542 + ... +212

sum of the series = 7182  

Step-by-step explanation:

This is an arithmetic series. The first term is known as 586 and the last term is known as 212. We are ask to find the sum of the series. The common difference of this sequence is -22 . The difference between the next term  and the previous term is -22. Let us find the number of terms.

common difference = 564 - 586 = -22

number of terms = n

nth term = a + (n - 1)d

212 = 586 + (n - 1)-22

212 = 586 - 22n + 22

212 - 586 - 22 = -22n

-396 = -22n

divide both sides by -22

n = -396/-22

n = 18

Using the formula for sum

sum of nth term = n/2(a + l)

where

l = last term

a = first term

n = number of term

sum of nth term = n/2(a + l)

sum of nth term = 18/2(586 + 212)

sum of nth term = 9(798 )

sum of the series = 7182  

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98