To find the sum of the odd integers between 14 and 58, you can use the formula for the sum of an arithmetic series:
Sum = (n/2) * [2a + (n-1)d]
In this case, 'a' is the first term (which is 15, the first odd integer greater than 14), 'n' is the number of terms, and 'd' is the common difference (which is 2 because we're dealing with odd numbers).
So,
a = 15
d = 2
To find 'n,' you can use the formula for the nth term of an arithmetic sequence:
nth term = a + (n-1)d
58 (the last term we want) = 15 + (n-1)2
Now, solve for 'n':
58 = 15 + 2n - 2
43 = 2n - 2
2n = 45
n = 22.5
Since 'n' should be a whole number (we can't have a fraction of a term), you need to round it down to 22. This means there are 22 odd integers between 14 and 58.
Now, plug these values into the sum formula:
Sum = (22/2) * [2 * 15 + (22-1) * 2]
Sum = 11 * [30 + 42]
Sum = 11 * 72
Sum = 792
So, the sum of the odd integers between 14 and 58 is 792.