Investigating Geometric Progressions?

📌 CONCEPT: A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

📐 RULE / FORMULA: The nth term of a geometric progression can be found using the formula: an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

💡 WORKED EXAMPLE: Consider the given sequence with a1 = 4 and r = 2. To find the fifth term, we use the formula an = a1 * r^(n-1). Substituting n = 5, a1 = 4, and r = 2, we get a5 = 4 * 2^(5-1) = 4 * 2^4 = 4 * 16 = 64.

⚠️ COMMON MISTAKE: Students often confuse the formula for the nth term of a geometric progression and incorrectly use an = a1 + r^(n-1).