Complete a sequence - up to 10

Learning Objectives Identify and differentiate between arithmetic and quadratic sequences. Calculate the common difference for an arithmetic sequence. Use the method of finite differences to identify a quadratic sequence and find its constant second difference. Determine the algebraic rule (nth term formula) for simple arithmetic and quadratic sequences. Accurately predict and calculate the next terms in a given sequence up to the 10th term. Apply pattern recognition skills to complete sequences that may not be arithmetic or quadratic. Ever noticed the patterns in a sunflower's seeds or the way a rumor spreads? 🌻 They all follow sequences! What number comes next in this pattern: 1, 4, 9, 16, ___? This tutorial will teach you how to decipher the hidden rules in number...

TermDefinitionExample SequenceAn ordered list of numbers, called terms, that follow a specific rule or pattern.The list 2, 4, 6, 8, 10, ... is a sequence. Term (a_n)Each individual number in a sequence. The subscript 'n' indicates the term's position (e.g., a_1 is the first term, a_5 is the fifth term).In the sequence 2, 4, 6, 8, ..., the third term (a_3) is 6. Arithmetic SequenceA sequence where the difference between any two consecutive terms is constant. This constant value is called the common difference.5, 9, 13, 17, ... is an arithmetic sequence with a common difference of 4. Common Difference (d)The constant value that is added to each term to get the next term in an arithmetic sequence.In the sequence 10, 7, 4, 1, ..., the common difference (d) is -3. Quadratic Sequ...

Arithmetic Sequence Formula (nth term) a_n = a_1 + (n-1)d Use this formula to find the value of any term (a_n) in an arithmetic sequence if you know the first term (a_1), the term's position (n), and the common difference (d). Quadratic Sequence Formula (nth term) a_n = An^2 + Bn + C This is the general form for any quadratic sequence. The key is to find the values of the coefficients A, B, and C using the method of finite differences. Finding Coefficients for a Quadratic Sequence A = (second difference) / 2 After finding the constant second difference using the method of finite differences, you can find the coefficient 'A' by dividing it by 2. You can then use a system of equations to find B and C.