Question

find the sum of the odd integers between 30 and 50.

the sum is \boxed{}.

Explanation:

Step1: Identify odd integers

Odd integers between 30 and 50: 31, 33, 35, 37, 39, 41, 43, 45, 47, 49.

Step2: Use arithmetic series formula

This is an arithmetic sequence with first term \(a_1 = 31\), last term \(a_n = 49\), common difference \(d = 2\).
Number of terms \(n\): \(a_n=a_1+(n - 1)d\)
\(49 = 31+(n - 1)\times2\)
\(18=(n - 1)\times2\)
\(n - 1 = 9\)
\(n = 10\)
Sum formula \(S_n=\frac{n(a_1 + a_n)}{2}\)
\(S_{10}=\frac{10\times(31 + 49)}{2}\)

Step3: Calculate the sum

\(S_{10}=\frac{10\times80}{2}=10\times40 = 400\)

Answer:

400