Find the sum of the odd integers from 1 through 49.
use what you know about arithmetic sequences, in this case
a = 1
d = 2
n = (49-1)/2 + 1 = 25
S25 = 25/2 (1+49)
To find the sum of the odd integers from 1 through 49, you can follow these steps:
1. Identify the first and last odd integers in the given range: The first odd integer is 1, and the last odd integer is 49.
2. Find the number of odd integers in the given range: To do this, subtract the first odd integer from the last odd integer and add 1. In this case: 49 - 1 + 1 = 49.
3. Use the formula for the sum of an arithmetic series: The sum of an arithmetic series is given by the formula: Sn = (n / 2) * (first term + last term), where Sn is the sum of the series, n is the number of terms, and the first and last terms are the first and last elements of the series, respectively.
4. Plug in the values into the formula: In this case, n = 49 (number of odd integers in the range), the first term = 1, and the last term = 49. Substituting these values into the formula, we get: Sn = (49 / 2) * (1 + 49).
5. Simplify and calculate: Sn = (24.5) * (50) = 1225.
Therefore, the sum of the odd integers from 1 through 49 is 1225.
To find the sum of the odd integers from 1 through 49, you can use a formula, which is based on the arithmetic series formula. The formula for the sum of an arithmetic series is:
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 odd integer is 1 and the last odd integer is 49. So, using the formula:
n = ((l - a) / 2) + 1
Substituting the values:
n = ((49 - 1) / 2) + 1
n = (48 / 2) + 1
n = 24 + 1
n = 25
Now that we know the number of terms (n), we can calculate the sum (Sn):
Sn = (n/2) * (a + l)
Sn = (25/2) * (1 + 49)
Sn = 12.5 * 50
Sn = 625
Therefore, the sum of the odd integers from 1 through 49 is 625.