Arithmetic Sequences

Arithmetic Sequences Choi 2012

Arithmetic Sequence • 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 Formulas In general: {a, a+d, a+2d, a+3d,...}

Example 1 – Arithmetic Sequence Given the formula for the term, find .

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

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.

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: 76, 85, ... 67, Explicit formula

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 76, 85, ... Therefore the sequences are: 67,

Example 6 – Applications of Arithmetic sequence • Find the general term of the following arithmetic sequence OR (5x - 3) (-2x - 1)

Homework: • P. 442 #6,7,8 (Every other), 9 • 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