Question

PLEASE HELP!!!

Every year, Mary and her family rent a cottage on a lake for their summer vacation. The first year, Mary paid $500. The second year she paid $515, and the third year she paid $530. If this pattern continues, how much money, total, will Mary have spent to rent the cottage every year for 20 years? You must show your work to receive full credit.

Answer 1

It goes up $15 every year. So that makes it $800. You would do 15 times 20 you would get 300. 500 plus 300 = $800

Answer 2

The total sum of money that Mary will have spent to rent the cottage every year for 20 years is $12850

Sequences and Series

Series are sum of sequences. The amount of money mary paid forms an arithmetic sequence given as:

500, 515, 530...

In order to determine the total amount of money she spend after 20years, we will find the sum of the first 20 years.

Given

First term "a" = 500

Difference "d" = 530 - 515 = 515 - 500
d = 15

n = 20

The formula for the sum of arithmetic sequence is given as:
Sn = n/2(2a+(n-1))d

Substitute

S20 = 20/2[2(500) + (20-1) * 15]
S20 = 10[1000 + 19(15)]

S20 = 10(1000 + 285)
S20 = 10(1285)
S20 = 12850

Hence the total sum of money that Mary will have spent to rent the cottage every year for 20 years is $12850

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