To calculate the sum of all odd numbers less than 50, we can use the arithmetic series formula. The formula for the sum of an arithmetic series is given by:
Sn = (n/2)(a + l)
where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term (a) is 1, the last term (l) is 49, and we need to find the number of terms
.
To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
an = a + (n-1)d
where an is the nth term, a is the first term, n is the number of terms, and d is the common difference.
In this case, the common difference (d) is 2, since we are dealing with odd numbers.
49 = 1 + (n-1)2
Simplifying the equation, we get:
48 = 2n - 2
Adding 2 to both sides, we have:
50 = 2n
Dividing both sides by 2, we get:
n = 25
Now that we have the number of terms, we can calculate the sum of the odd numbers less than 50:
Sn = (n/2)(a + l)
= (25/2)(1 + 49)
= (25/2)(50)
= 625
So, the sum of all odd numbers less than 50 is 625.
Sn = (n/2)(a + l)
where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term (a) is 1, the last term (l) is 49, and we need to find the number of terms
.To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
an = a + (n-1)d
where an is the nth term, a is the first term, n is the number of terms, and d is the common difference.
In this case, the common difference (d) is 2, since we are dealing with odd numbers.
49 = 1 + (n-1)2
Simplifying the equation, we get:
48 = 2n - 2
Adding 2 to both sides, we have:
50 = 2n
Dividing both sides by 2, we get:
n = 25
Now that we have the number of terms, we can calculate the sum of the odd numbers less than 50:
Sn = (n/2)(a + l)
= (25/2)(1 + 49)
= (25/2)(50)
= 625
So, the sum of all odd numbers less than 50 is 625.