Student save $1 on the first day, $2 on the second day and $3 on the third day and so on
What will be his total savings in 365 days
The student is saving $1 more each day for a total of 365 days. We can calculate the total savings by using the formula for the sum of an arithmetic series:
n/2(a + l),
where n is the number of terms, a is the first term, and l is the last term.
In this case, we have n = 365, a = 1, and l = 365.
By plugging in these values, we find:
365/2(1 + 365)
= 182.5(366)
= 66,795.
Therefore, the student will have a total savings of $66,795 in 365 days.
To find the student's total savings in 365 days, we can use the formula for the sum of an arithmetic series.
The sum of an arithmetic series can be calculated using the formula:
Sn = (n/2)(a + L)
Where:
Sn is the sum of the series
n is the number of terms
a is the first term
L is the last term
In this case, the student saves $1 on the first day, and the amount saved increases by $1 each day. So, the first term (a) is $1 and the last term (L) is $365.
Using the formula, we can calculate the sum:
Sn = (365/2)(1 + 365)
= (365/2)(366)
= 66795
Therefore, the student's total savings in 365 days would be $66,795.
To find out the total savings in 365 days, you need to calculate the sum of savings from Day 1 to Day 365.
Here's how you can do it:
Step 1: Determine the savings for each day using the given pattern.
- Day 1: $1
- Day 2: $2
- Day 3: $3
- Day 4: $4
- ...and so on...
Step 2: Since the amount saved increases by $1 each day, we can consider this as an arithmetic sequence with a common difference of 1. The formula to calculate the sum of an arithmetic sequence is:
Sn = (n/2)(2a + (n - 1)d)
Where:
Sn = sum of the sequence
n = number of terms in the sequence
a = first term of the sequence
d = common difference
Step 3: Apply the formula. In this case, the first term (a) is $1, the common difference (d) is $1, and the number of terms (n) is 365.
Sn = (365/2)(2(1) + (365 - 1)(1))
Step 4: Simplify the equation.
Sn = (365/2)(2 + 364)
Step 5: Calculate.
Sn = (365/2)(366)
= 66,795
Therefore, the total savings in 365 days will be $66,795.