Write the addition sentence - up to two digits

Learning Objectives Identify an arithmetic sequence and determine its common difference, including two-digit integers. Formulate the recursive addition sentence (a_n = a_{n-1} + d) for any given arithmetic sequence. Translate a recursive addition sentence into the explicit formula for the nth term (a_n = a_1 + (n-1)d). Apply the addition sentence and explicit formula to find missing or future terms in a sequence. Determine the addition sentence when given two non-consecutive terms of an arithmetic sequence. Model real-world linear growth scenarios using arithmetic sequences and their corresponding addition sentences. Ever notice how a stack of chairs grows by the same height with each added chair? 📏 How can we write a single mathematical sentence to describe that predictabl...

TermDefinitionExample Arithmetic SequenceAn ordered list of numbers in which the difference between any two consecutive terms is constant.The sequence -4, 2, 8, 14, 20, ... is an arithmetic sequence because you always add 6 to get to the next term. Term (a_n)An individual number in a sequence. The notation 'a_n' refers to the term in the nth position.In the sequence 10, 20, 30, 40, ..., the third term is written as a_3 = 30. Common Difference (d)The constant value that is added to a term to get the next term in an arithmetic sequence. It can be positive or negative.In the sequence 150, 125, 100, 75, ..., the common difference is d = -25. Recursive Addition SentenceA rule that defines a term in a sequence by relating it to the term that came immediately before it. It always requi...

Finding the Common Difference d = a_n - a_{n-1} To find the common difference (d), subtract any term from the term that immediately follows it. This is the first step to writing the addition sentence for an arithmetic sequence. The Recursive Addition Sentence a_n = a_{n-1} + d This formula defines the 'next' term (a_n) by taking the 'previous' term (a_{n-1}) and adding the common difference (d). It describes the step-by-step pattern of the sequence. The Explicit Formula a_n = a_1 + (n-1)d This powerful formula allows you to find the value of any term (a_n) directly, as long as you know the first term (a_1), the position of the term you want (n), and the common difference (d).