Complete an increasing number sequence

Learning Objectives Identify if an increasing sequence is arithmetic, geometric, or quadratic. Calculate the common difference, common ratio, or constant second difference for a sequence. Derive the algebraic formula (nth term) for linear and quadratic sequences. Use the derived formula to find any missing term in an increasing number sequence. Extend a given sequence by determining the next consecutive terms. Apply sequence-completion skills to solve pattern-based problems. Ever noticed how a viral video's views seem to explode overnight? 📈 The pattern of that growth can often be described by a mathematical sequence! In this tutorial, you will move beyond simple patterns to master the techniques for completing more complex increasing number sequences, including those...

TermDefinitionExample Increasing SequenceA sequence of numbers where each term is greater than the previous term. The values are always going up.2, 4, 8, 16, 32, ... TermAn individual number, variable, or expression in a sequence. We use the notation 'a_n' to denote the nth term.In the sequence 5, 10, 15, 20, ..., the third term (a_3) is 15. Arithmetic SequenceA sequence where the difference between any two consecutive terms is constant. This constant is called the common difference (d).3, 7, 11, 15, ... (The common difference is 4). Geometric SequenceA sequence where the ratio between any two consecutive terms is constant. This constant is called the common ratio (r).2, 6, 18, 54, ... (The common ratio is 3). Quadratic SequenceA sequence whose nth term is a quadratic expression...

Arithmetic Sequence nth Term Formula a_n = a_1 + (n-1)d Use this formula to find the value of any term (a_n) in an arithmetic sequence. You need the first term (a_1), the term number you want to find (n), and the common difference (d). Geometric Sequence nth Term Formula a_n = a_1 * r^(n-1) Use this formula to find the value of any term (a_n) in a geometric sequence. You need the first term (a_1), the term number (n), and the common ratio (r). Quadratic Sequence nth Term Form a_n = An^2 + Bn + C This is the general form for a quadratic sequence. The coefficient A is half of the constant second difference (A = second_difference / 2). B and C can be found by setting up and solving a system of equations.