Complete a geometric number sequence

Learning Objectives Identify if a sequence is geometric by checking for a common ratio. Calculate the common ratio of a geometric sequence, including negative and fractional ratios. Determine the next terms in a given geometric sequence. Find missing terms within a geometric sequence using the common ratio or the concept of a geometric mean. Apply the nth term formula to find any specific term in a geometric sequence. Solve problems where two non-consecutive terms are given to complete the sequence. If a single social media post doubles its shares every hour, how many people will have shared it by the end of the day? 🤔 This is the power of geometric sequences! This tutorial will teach you how to identify, analyze, and complete geometric number sequences. Understanding thes...

TermDefinitionExample SequenceAn ordered list of numbers, where each number is called a term.The list 2, 4, 6, 8, 10, ... is a sequence. TermAn individual number or element in a sequence. The first term is often denoted as a₁, the second as a₂, and the nth term as aₙ.In the sequence 3, 9, 27, ..., the first term (a₁) is 3 and the third term (a₃) is 27. Geometric SequenceA sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number.The sequence 5, 10, 20, 40, ... is geometric because you multiply by 2 each time. Common Ratio (r)The fixed number that you multiply by to get from one term to the next in a geometric sequence.In the sequence 100, 50, 25, ..., the common ratio is 1/2 because 100 * (1/2) = 50. nth Term (aₙ)A formula or expression...

Common Ratio Formula r = a_n / a_{n-1} To find the common ratio (r), divide any term by the term that comes directly before it. This is the most fundamental step in analyzing a geometric sequence. The nth Term Formula a_n = a_1 * r^(n-1) Use this formula to find the value of any term (aₙ) in a geometric sequence if you know the first term (a₁), the common ratio (r), and the term number (n) you want to find.