Questions on Arithmetic Sequences and Series - College Algebra | MATH 140, Study notes of Algebra

Download Questions on Arithmetic Sequences and Series - College Algebra | MATH 140 and more Study notes Algebra in PDF only on Docsity! Math 140 E2 Dec.1,2008 10.2 Arithmetic Sequences and Series 1. Arithmetic Sequences: An arithmetic sequence is a sequence in which the difference between any two successive terms is the same, i.e., the difference is a constant. That is an+1 − an = d for any integer n ≥ 1, where the constant d is called the common difference Example1:(1) 4, 7, 10, 13, · · · (2){an} = {4− n} 2. nth Term of an Arithmetic Sequence an = a1 + (n− 1)d Example2: Find the thirteenth term of the sequence 2, 6, 10, 14, 18, · · · Example3: The 3rd term of an arithmetic sequence is 8, and the 16th term is 47. Find a1 and d and construct the sequence. 3. Sum of n Terms of an Arithmetic Sequence Let {an} be an arithmetic sequence with first term a and common difference d. The sum Sn of the first n terms of {an} is Sn = n 2 [2a + (n− 1)d] = n 2 (a + an) Example3:(1) Find the sum of the first 15 terms of the arithmetic sequence 8, 11, 14, 17, · · · (2) 100∑ k=1 (2k − 1) (3) Suppose that you just received a job offer with a starting salary of $35,000 per year and a guaranteed raise of $1400 per year. How many years will it take before your aggregate salary is $280,000? 1