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Answer :
To calculate the total number of minutes Sasha reads during the 30 days, we need to find the sum of the arithmetic sequence where each term represents the number of minutes Sasha reads each day. The common difference between consecutive terms is 5 (Sasha reads 5 minutes longer each day), and the first term is 20 minutes.
The formula to find the sum of an arithmetic sequence is:
Sum = (n/2) * (2a + (n-1)d)
where:
n = number of terms
a = first term
d = common difference
In this case, we have:
n = 30 (since Sasha reads for 30 days)
a = 20 (the first day's reading time)
d = 5 (the difference in reading time each day)
Plugging in the values into the formula:
Sum = (30/2) * (2*20 + (30-1)*5)
Simplifying the expression:
Sum = 15 * (40 + 29*5)
Sum = 15 * (40 + 145)
Sum = 15 * 185
Sum = 2775
Therefore, Sasha reads a total of 2775 minutes during the 30 days.
Learn more about arithmetic sequence here:
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Sasha reads a total of 2775 minutes during the 30 days.
To solve this problem, we can recognize that the total number of minutes Sasha reads forms an arithmetic series where the first term, [tex]\( a_1 \)[/tex], is 20 minutes and the common difference, d, is 5 minutes. The number of terms, n, is 30 since Sasha reads for 30 days.
The sum of the arithmetic series is:
[tex]\[ S_n = \frac{n}{2} \times (a_1 + a_n) \][/tex]
where [tex]\( a_n \)[/tex] is the last term of the series.
Since the first term is 20 minutes and the common difference is 5 minutes, the last term [tex]\( a_n \)[/tex] can be calculated as:
[tex]\[ a_n = a_1 + (n - 1)d \] \[ a_n = 20 + (30 - 1) \times 5 \] \[ a_n = 20 + 29 \times 5 \] \[ a_n = 20 + 145 \] \[ a_n = 165 \][/tex]
Now we can calculate the total minutes Sasha reads:
[tex]\[ S_n = \frac{30}{2} \times (20 + 165) \] \[ S_n = 15 \times 185 \] \[ S_n = 2775 \][/tex]
Therefore, Sasha reads a total of 2775 minutes during the 30 days.
