Consider a geometric progression, where a1 represents the first term, and an represents the nth term. Each term of the progression is defined by the product of the previous term and the common ratio, r. The derivation of the formula for the finite sum of a geometric progression, where r < 1, is shown below, with a mistake at a key step. Steps Derivation Reasons 1 Given 2 Substitution 3 Multiply both sides by r 4 Subtracting Sr from S 5 Factor common terms 6 Division Determine the step where the first mistake occurs.