Geometric sequences with fractions

Learning Objectives Identify if a sequence containing fractions is geometric. Calculate the common ratio (r) when it is a fraction. Determine the next term in a geometric sequence involving fractions. Use the general term formula, a_n = a_1 * r^(n-1), to find a specific term when a_1 and/or r are fractions. Determine a missing term within a geometric sequence of fractions. Set up and solve simple real-world problems that model geometric sequences with fractions. Imagine a pizza is shared so that each person takes 1/3 of the remaining amount. How much is left for the 4th person? 🍕 This tutorial explores geometric sequences where the numbers are fractions or the pattern involves multiplying by a fraction. Understanding these sequences is crucial for grasping concepts like ex...

TermDefinitionExample Geometric SequenceA sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number.The sequence 32, 16, 8, 4, ... is geometric because you multiply by 1/2 each time. Term (a_n)Each individual number in a sequence. We use a_1 for the first term, a_2 for the second, and a_n for the nth term.In the sequence 1/2, 1/4, 1/8, the third term (a_3) is 1/8. Common Ratio (r)The constant factor you multiply by to get from one term to the next. It is found by dividing any term by its preceding term.In the sequence 81, 27, 9, ..., the common ratio is r = 27/81 = 1/3. First Term (a_1)The starting value or the very first number in a sequence.In 1/5, 1/10, 1/20, ..., the first term (a_1) is 1/5. Fractional RatioA common ratio...

Finding the Common Ratio (r) r = a_n / a_{n-1} To find the common ratio, divide any term by the term that comes directly before it. This is the key to proving a sequence is geometric and finding the pattern. The General Term Formula a_n = a_1 * r^(n-1) This formula allows you to find any term (a_n) in a geometric sequence if you know the first term (a_1), the common ratio (r), and the term number you want (n).