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Arithmetic Sequences & Partial Sums

Section 8.2 Arithmetic Sequences & Partial Sums

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Arithmetic Sequences & Partial Sums

A sequence in which a set number is added to each previous term is called an arithmetic sequence. Definition of Arithmetic Sequences A sequence is arithmetic if the difference between consecutive terms are the same. So, the sequence a1, a2, a3, a4, …, an, … Is arithmetic if there is a number d such that a2 – a1= a3 – a2 = a4 – a3 = … = d

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Arithmetic Sequences & Partial Sums

Examples: Determine if the following sequences are arithmetic, and if so, determine the common difference, d.

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Arithmetic Sequences & Partial Sums

How does one determine a particular term in a given sequence? The nth term of an Arithmetic Sequence The nth term of an arithmetic sequence has the form an = a1 + (n – 1)d where d is the common difference between consecutive terms of the sequence.

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Arithmetic Sequences & Partial Sums

Examples: 1. Find the 40th term of the sequence where a1 = 4 and d = – 2. 2. Determine the formula for the sequence described in #1. Note: In developing a formula, only substitute for a1 and d. Then simplify.

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Arithmetic Sequences & Partial Sums

The Sum of a Finite Arithmetic Sequence The sum of a finite arithmetic sequence with n terms is given by

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Arithmetic Sequences & Partial Sums

Examples: 1. Find the sum of the first 20 multiples of 4. 2. Find the sum of the 10 terms defined by an = 3n – 4

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Arithmetic Sequence & Partial Sum

Example: An auditorium has 30 rows of seats. There are 15 seats in the first row and then an additional seat added on each end in each row thereafter. What is the seating capacity of the auditorium?

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Arithmetic Sequences & Partial Sums

What you should know: 1. Apply the formula for an arithmetic sequence. 2. Apply the formula for finding the nth partial sum of an arithmetic sequence.

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