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?

Let  represent the number of pages Sasha reads in day n

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

in the first day Sasha reads 20 minutes means minutes

minutes, since Sasha reads 5 minutes more than day 1

so we can make the following list:

 




so clearly

in 30 days Sasha reads:

+++...+=

= 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

1035 minutes