Lesson Plan

Write the explicit rule aₙ = a₁·r^(n−1) for a geometric sequence and use it to find any term, and use Sₙ = a₁(1 − rⁿ)/(1 − r) to find the sum of the first n terms

Test whether a sequence is geometric by computing all consecutive ratios, state the common ratio including when it is negative or fractional, and distinguish a geometric sequence (exponential in its index) from an arithmetic one (linear)

Write the recursive rule aₙ = r·aₙ₋₁ (with a₁ stated) and distinguish it from the explicit rule

Find r, a₁, or a missing term from two given terms, recognizing when an even gap count admits two possible ratios

Determine whether an infinite geometric series converges by testing |r| < 1, and compute S∞ = a₁/(1 − r) when it does

Translate a percentage growth or decay rate into a common ratio and solve ACT-style compound-interest, half-life, and depreciation problems

F 301. Extend a given pattern by a few terms for patterns that have a constant factor between terms F 703. Exhibit knowledge of geometric sequences F 502. Find the next term in a sequence described recursively F 603. Find a recursive expression for the general term in a sequence described recursively F 702. Build functions for relations that are exponential A 512. Work problems involving positive integer exponents AF 601. Solve word problems containing several rates, proportions, or percentages