In order to use Formula 1, the number of terms must be known. The first multiple of 3 between 28 and 112 is 30, and the last multiple of 3 between 28 and 112 is 111. In the arithmetic sequence –3, 4, 11, 18, …, find the sum of the first 20 terms.įind the sum of the multiples of 3 between 28 and 112. This formula for the sum of an arithmetic sequence requires the first term, the common difference, and the number of terms. Substituting this last expression for ( a 1 + a n) into Formula 1, another formula for the sum of an arithmetic sequence is formed. This formula requires the values of the first and last terms and the number of terms. If S nrepresents the sum of an arithmetic sequence with terms, then Following is a simple formula for finding the sum:
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