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?
Mathematics · College · Tue Nov 03 2020
Answered on
Formula :
Sum of AP = (n/2) (2a + (n - 1)d)
We have a = 10,
d = 3,
n = ?
(n/2) (20 +(n - 1) 3) < 900
n(20 +3n-3) < 1800
3n²-17n < 1800
Use the quadratic equation to solve
3n-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
So, amount needed to reach $900 = $(900 - 840)
= $60
So, Dreya need to save $60 in her final week of saving.