Question

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?

Answer 1

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
 

Answer 2

The total minutes she can read would be 1035 minutes.

What is the fundamental principle of multiplication?

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Let consider dn the number of pages Sasha reads in day n.

For the first day Sasha reads 20 minutes means d1 = 20minutes

So, d2 = 20 + 5 = 25 minutes

Since Sasha reads 5 minutes more than day 1 so we can make the following list as;

d1 = 20minutes

d2 = 25 minutes

d3 = 20 + 5 + 5 = 30 minutes

This makes a sequence as

dn = 20 + (n-1) d

AS

d1 + d2 + d3 +....d30 = 20 +(20+5)+(20+5*2)+(20+5*3)+...+(20+5*29)

Now, we have in the 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

20*30 + 435 = 600 + 435 = 1035 (minutes)

The total minutes she can read would be 1035 minutes.

Learn more about multiplications;

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