Finding the Ratio
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 41 of 49.
If you know two neighbouring terms, you know the ratio: divide the later one by the earlier one. In 7, 28, 112, ..., the ratio is 28/7, which is 4. Check it on the next pair: 112/28 is 4 as well.
The order matters. Dividing the earlier term by the later one gives 1/4, the ratio for walking backwards. The ratio can also be a fraction or negative: in 48, 12, ..., it is 12/48 = 1/4, and in 2, -6, 18, ..., it is -6/2 = -3, so the signs take turns.
This is also how you tell the two kinds of sequence apart. Subtract neighbours: the same answer each time means arithmetic. Divide neighbours: the same answer each time means geometric.
Challenge
Two neighbouring terms of a geometric sequence are 18 and then 54. Find the common ratio r. On the blank board, write an r = ... line as a division, then a line with its value.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponentials, Logs & Sequences
1Exponential Functions
Repeated MultiplyingGrowth or DecayDrawing GrowthDrawing DecayRecap: Exponential Functions3Same-Base Equations
Matching PowersRewriting the BaseAn Expression UpstairsFractions and NegativesRecap: Same Base9Geometric Sequences
Multiply Each TimeFinding the RatioGeometric SumsForever SumsRecap: Geometric Sequences