Section 8.2 Arithmetic Sequences & Partial Sums

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 a 1, a 2, a 3, a 4, …, a n, … Is arithmetic if there is a number d such that a 2 – a 1 = a 3 – a 2 = a 4 – a 3 = … = d

Arithmetic Sequences & Partial Sums Examples: Determine if the following sequences are arithmetic, and if so, determine the common difference, d.

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 a n = a 1 + (n – 1)d where d is the common difference between consecutive terms of the sequence.

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

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

Arithmetic Sequences & Partial Sums Examples: 1. Find the sum of the first 20 multiples of Find the sum of the 10 terms defined by a n = 3n – 4

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?

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.

Homework Page even, odd, 36, 38, 44, even, odd