Warm Up Complete the table… Recursive Formula Sequence

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Warm Up Complete the table… Recursive Formula Sequence Explicit Formula 6,8,10,12…

Arithmetic Sequences and Partial Sums Keeper GSE Accelerated Pre-Calculus

Arithmetic Sequences A sequence is arithmetic if there exists a number d, called the common difference, such that an+1 = an + d

Example For each of the following arithmetic sequences, identify the first term, a1, and the common difference, d. a) 6, 10, 14, 18, 22, … b) 0, 6, 12, 18, 24, … c)

nth Term of an Arithmetic Sequence The nth term of an arithmetic sequence is given by the formula: an = a1 + (n  1)d

Example Find the 11th term of the arithmetic sequence 2, 6, 10, 14, …

Another Example The 3rd term of an arithmetic sequence is 5, and the 9th term is 37. Find a1 and d and construct the sequence.

Sum of the First n Terms The formula for the sum of the first n terms of an arithmetic sequence is given by:

Example Find the sum of the first 11 terms of the arithmetic sequence 16, 12, 8, 4, …

Another Example Find the sum:

Application An orchestra consists of 8 rows of musicians. The first row has 5 musicians, the second row has 7 musicians, and the third row has 9 musicians. a) How many musicians are in the last row? b) What is the total number of musicians in the orchestra?