 # 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.

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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,...}. n n 19  Explicit formula Method 2

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 (1)(2) Substitute into (1) Therefore the sequences are: 67, 76,85,...  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 Therefore the sequences are:67, 76,85,...  t n=121+(n-7)d  t 1 = 121+(1-7)d To find a, we use the same thinking process!!

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: 1)Solve the following equation 2)How many consecutive natural numbers, starting with 1, need to be added to produce a sum of 153? Answers: 1)40 terms, y = 1 2)17

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