Problem

Find the sum of the first 20 terms of the arithmetic sequence defined by the function f(n)=3n+1

Answer

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Answer

Finally, use the formula for the sum of an arithmetic sequence: Sn=n2(a1+an). Substituting n=20, a1=4, and a20=61 into the formula gives S20=202(4+61)=10(65)=650

Steps

Step 1 ：First, calculate the first term of the sequence using the function f(n). When n=1, the first term a1=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 a20=f(20)=3(20)+1=61

Step 3 ：Finally, use the formula for the sum of an arithmetic sequence: Sn=n2(a1+an). Substituting n=20, a1=4, and a20=61 into the formula gives S20=202(4+61)=10(65)=650

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