Finding the nth Term

Algebra 2 · Axiom Academy

EXAMPLE Finding the nth Term of an Arithmetic Sequence Deriving an explicit formula for the sequence Find an explicit formula for the n th term, a_n , of the arithmetic sequence Then use the formula to predict the next term. Nice work — you derived the explicit formula for an arithmetic sequence from its first few terms. Remember: Constant difference: arithmetic sequences add the same value d to get from one term to the next. Two ingredients: once you know a_1 and d , the formula a_n=a_1+(n-1)d finds any term directly — no need to list every term in between. Simplify: distributing turns a_n=a_1+(n-1)d into a clean linear form like a_n=4n-1 . Always verify: test the formula against a term you can also find by continuing the pattern — here a_5=19 matches 15+4 . This same two-step process — find a_1 and d , then plug into the formula — works for every arithmetic sequence you'll meet.

This is the written version of the interactive lesson above. See the full Algebra 2 course.