Dreya is saving money to purchase a $900 computer, and she saves $10 the first week. each week after that, she saves $3 more than the previous week, except in the last week, when she reaches $900. to have a final sum of exactly $900, how much money does dreya need to save in her final week of saving?

Sum of AP =

(n/2) (2a + (n - 1)d)

You have a = 10, d = 3, and want to know how long to reach a total of 900.

(n/2) (20 + (n - 1) 3) < 900

n(20 + 3n - 3) < 1800

3n² - 17n < 1800

Use the quadratic equation to solve

3n² - 17n - 1800 = 0, which gives

n = 21.8

so to get less than 0 on the right-hand side, 21 is the nearest integer.

Thus, in 21 weeks, she saves a total of

(21/2) (2*10 + (20)3)

= (21/2) (80) = 840

which leaves her 60 to save in week 22.

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