Find terms of a geometric sequence

Learning Objectives Define a geometric sequence and identify its first term (a₁) and common ratio (r). Calculate the common ratio of a geometric sequence given any two consecutive terms. Apply the explicit formula to find any specified term (the nth term) of a geometric sequence. Determine the first term or common ratio when given two non-consecutive terms in a sequence. Find a missing term between two non-consecutive terms (a geometric mean). Solve real-world problems that model geometric growth or decay by finding a specific term. Ever see a video go viral, jumping from 100 views to 10,000 in just a few shares? 📈 That explosive growth is a perfect example of a geometric sequence at work! This tutorial will teach you the fundamentals of geometric sequences, which are sequ...

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 called the common ratio.The sequence 5, 10, 20, 40, ... is a geometric sequence because each term is multiplied by 2 to get the next term. Term (aₙ)An individual number or element in a sequence. The subscript 'n' denotes the term's position in the sequence.In the sequence 5, 10, 20, 40, ..., the third term is a₃ = 20. First Term (a₁)The very first number in a sequence.In the sequence 5, 10, 20, 40, ..., the first term is a₁ = 5. Common Ratio (r)The constant, non-zero number that is multiplied by each term to get the next term. It is found by dividing any term by its preceding term (r = aₙ / aₙ₋₁).In the sequence 5...

Common Ratio Formula r = aₙ / aₙ₋₁ Use this formula to find the common ratio (r). Simply divide any term in the sequence by the term that comes immediately before it. This should be constant for the entire sequence. Explicit Formula for the nth Term aₙ = a₁ * r^(n-1) This is the most important formula for finding terms. Use it to calculate the value of any term (aₙ) when you know the first term (a₁), the common ratio (r), and the position of the term you want to find (n).