Multiply Each Time
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 40 of 49.
The list 2, 10, 50, 250, ... multiplies by 5 each time. A list like this is a geometric sequence, and the number it multiplies by is its common ratio r. Here the first term is 2 and r is 5.
The 5th term is 4 multiplications after the first, because the first term has not been multiplied at all. So it is 2 × 5^4. Work the power first: 5^4 is 625, and 2 times 625 is 1250. Multiplying 2 by 5 first would give 10^4, a different number. In general, with a(1) the first term,
a(n) = a(1) × r^(n - 1)
Written as a function, the rule for 2, 10, 50, ... is a(n) = 2 × 5^(n - 1).
Challenge
The sequence 3, 6, 12, ... has the rule a(n) = 3 × 2^(n - 1). Work out a(6), its 6th 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
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