Grade 11 Functions (MCR3U) Unit 5: Pascal’s Triangle, Binomial Theorem, Sequences & Series Arithmetic Sequences Mr. Choi © 2018 E. Choi – MCR3U - All Rights Reserved

Arithmetic Sequence {a, a+d, a+2d, a+3d,...} A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence. In an arithmetic sequence, the first term t1, is denoted as a. Each term after the first is found by adding a constant, called the common difference, d, to the preceding term. The list then becomes . {a, a+d, a+2d, a+3d,...} Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Arithmetic Sequences Formulas In general: {a, a+d, a+2d, a+3d,...} Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Example 1 – Arithmetic Sequence Given the formula for the term, find . Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Example 2 – Finding Formula for the nth term Find the formula for the term, , and find that determines the following arithmetic sequence {8, 12, 16, 20, ...}. Method 2 19 19 n n 19 19 Explicit formula Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Example 3 – Find number of terms in the sequence How many terms are there in the following sequences? {-3, 2, 7, ..., 152}. There are 32 terms in the sequence. Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Example 4 – Find the terms in the sequence In an arithmetic sequence, t7 = 121 and t 15 = 193. Find the first 3 terms of the sequence and . 2 - 1 Substitute into (1) (1) (2) Therefore the sequences are: 67, 76, 85, ... Arithmetic Sequences Explicit formula © 2018 E. Choi – MCR3U - All Rights Reserved

Example 5 – Find the terms in the sequence In an arithmetic sequence, t7 = 121 and t 15 = 193. Find the first 3 terms of the sequence and . METHOD 2 To find a, we use the same thinking process!! t1 = 121+(1-7)d tn=121+(n-7)d Therefore the sequences are: 67, 76, 85, ... Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Example 6 – Applications of Arithmetic sequence Find the general term of the following arithmetic sequence OR (5x - 3) (-2x - 1) Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

Homework: Text Book: P. 385 #1 - 12 Work Sheet: Check the website for updates Extra questions: Solve the following equation How many consecutive natural numbers, starting with 1, need to be added to produce a sum of 153? Answers: 40 terms, y = 1 17 Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

End of Lesson Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved