Finding Geometric Sequence Terms

Pre-Calculus · Axiom Academy

EXAMPLE Finding Geometric Sequence Terms Work out which term of a geometric sequence equals a given value by solving for n . In the geometric sequence , which term equals ? In other words, find the position n for which . Nice work — you found that is the 10th term . Every geometric-sequence question reduces to the same explicit formula; what you solve for just changes. The one formula: — the exponent is n-1 , one less than the term number. Finding a specific term: substitute a_1 , r , and n . For example, with , the 8th term is . Finding the common ratio: set up the equation, isolate , then take the matching root. If a_1=1000 and a_5=62.5 , then , so . Finding which term: set a_n equal to the target, isolate the power, and match exponents on the same base — which is exactly what gave us n=10 here. Growth vs. decay: if the terms grow; if they shrink toward 0 , as does above. Once a sequence is written as , every "find the term / find r / find n " question is just algebra on that single relationship.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.