Find the sum of the first 20 terms of the arithmetic sequence defined by the function \(f(n) = 3n+1\)
Answer
Finally, use the formula for the sum of an arithmetic sequence: \(S_n = \frac{n}{2}(a_1 + a_n)\). Substituting \(n=20\), \(a_1=4\), and \(a_{20}=61\) into the formula gives \(S_{20} = \frac{20}{2}(4 + 61) = 10(65) = 650\)
Step 1 ：First, calculate the first term of the sequence using the function \(f(n)\). When \(n=1\), the first term \(a_1 = f(1) = 3(1)+1 = 4\)
Step 2 ：Next, calculate the 20th term of the sequence using the function \(f(n)\). When \(n=20\), the 20th term \(a_{20} = f(20) = 3(20)+1 = 61\)
Step 3 ：Finally, use the formula for the sum of an arithmetic sequence: \(S_n = \frac{n}{2}(a_1 + a_n)\). Substituting \(n=20\), \(a_1=4\), and \(a_{20}=61\) into the formula gives \(S_{20} = \frac{20}{2}(4 + 61) = 10(65) = 650\)
