The nth Term
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 36 of 49.
The list 2, 5, 8, 11, ... adds 3 each time. A list that changes by the same amount at every step is an arithmetic sequence, and the amount is its common difference d. Here the first term is 2 and d is 3.
To reach the 10th term you do not need to write out ten numbers. Starting from 2, the 10th term is 9 steps along, because the first term took no steps at all. So it is 2 + 9 × 3, which is 29. In general, with a(1) the first term, the term in position n is
a(n) = a(1) + (n - 1) × d
Written as a function, the rule for 2, 5, 8, ... is a(n) = 2 + (n - 1) × 3, and a(10) is its 10th term.
Challenge
The sequence 7, 11, 15, ... has the rule a(n) = 7 + (n - 1) × 4. Work out a(15), its 15th term. Tap the move that uses the rule, then type the arithmetic line by line.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponentials, Logs & Sequences
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