find the sum of the integers from 8 to 35
Answer (1)
Step 1: Calculate the number of terms in the series. The number of terms \(n\) in the series from \(a\) to \(b\) is given by \(n=b-a+1\). In this case, \(a=8\) and \(b=35\). Therefore, \(n=35-8+1=28\). Step 2: Calculate the sum of the series. The sum \(S\) of an arithmetic series with \(n\) terms, first term \(a_{1}\), and last term \(a_{n}\) is given by \(S=\frac{n}{2}(a_{1}+a_{n})\). In this case, \(n=28\), \(a_{1}=8\), and \(a_{n}=35\). Therefore, \(S=\frac{28}{2}(8+35)\). Step 3: Simplify the expression. \(S=14(43)\). \(S=602\).
