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Rainbow [258]
2 years ago
11

Sasha sets a goal to read 5 minutes longer than each previous day for 30 days. On the first day, Sasha reads for 20 minutes. The

expression mc018-1.jpg represents the total number of minutes Sasha reads during the 30 days. How many total minutes does she read?
Mathematics
2 answers:
Serjik [45]2 years ago
0 0
Let d_n represent the number of pages Sasha reads in day n

for example d_7 is the number of pages that Sasha read in day 7.

in the first day Sasha reads 20 minutes means d_1=20 minutes


d_2=20+5=25 minutes, since Sasha reads 5 minutes more than day 1

so we can make the following list:

d_1=20 
d_2=20+5
d_3=20++5+5=20+5*2
d_4=20+5+5+5=20+5*3

so clearly d_n=20+5(n-1)

in 30 days Sasha reads:

d_1+d_2+d_3+...+d_3_0=

= 20 +(20+5)+(20+5*2)+(20+5*3)+...+(20+5*29)

we have in total 30 twenties + 5(1+2+3+....+29), factorizing 5.

the sum 1+2+3+....+29 can be found by Gauss formula as (29*30)/2 = 435

So the total sum is 20*30+435=600+435=1035 (minutes)

Remark: Gauss formula states that 1+2+3+...+(n-1)+n = n(n+1)/2


Answer: 1035 minutes
 
NNADVOKAT [17]2 years ago
0 0

Correct answer is 2,775 on en

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