4-7 Arithmetic Sequences
Sequence: is an ordered list of numbers that often form a pattern Term of a Sequence: What each number in the list is called
Arithmetic Sequence: The difference between consecutive terms is constant This difference is called the Common Difference
Problem 1 and 2: Extending Sequences and Identifying Arithmetic Sequences Tell whether the sequence is arithmetic. If it is find the common difference and find the next three terms. 3, 8, 13, 18, …
Tell whether the sequence is arithmetic Tell whether the sequence is arithmetic. If it is find the common difference and find the next three terms. 6, 9, 13, 17
Tell whether the sequence is arithmetic Tell whether the sequence is arithmetic. If it is find the common difference and find the next three terms. 8, 15, 22, 30
Tell whether the sequence is arithmetic Tell whether the sequence is arithmetic. If it is find the common difference and find the next three terms. 10, 4, –2, –8
Problem 3: Writing a Recursive Formula 𝐴 𝑛 =𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒 𝐴 𝑛 =𝐴 𝑛−1 +𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
Write a recursive formula for the arithmetic sequence 70, 77, 84, 91, …
Write a recursive formula for the arithmetic sequence 97, 88, 79, 70, …
Problem 4: Writing an Explicit Formula The common difference of the sequence The 1st term of the sequence
Write an explicit formula for the arithmetic sequence 3, 7, 11, 15, …
Write an explicit formula for the arithmetic sequence 3, −2, −7, −12, …