Finding the 50th Term

Algebra 1 · Axiom Academy

Find any term in an arithmetic sequence with the formula a_n = a_1 + (n-1)d . Given the arithmetic sequence below, find the 50th term a_ 50 . Nice work — you found any term of an arithmetic sequence straight from the formula. Constant gap: An arithmetic sequence adds the same common difference d between consecutive terms. The formula: a_n = a_1 + (n-1)d , using the first term a_1 , the common difference d , and the term number n . Result: With a_1 = 3 and d = 4 , the 50th term is a_ 50 = 3 + (50-1)(4) = 199 . The same formula finds the 10th, 100th, or any term — just substitute that term number for n .

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