Arithmetic Sequences

Part 2Arithmetic SequencesArithmetic SequencesRemember an arithmetic sequence is found by adding the same number over and over again.That number is called d the common difference.The formula for finding the general term is:an = a1 + (n 1)dArithmetic SequencesNow we will use the general term formula to find specific terms in an arithmetic sequence.Find the 13th term of the sequence 2, 5, 8, 11, an = a1 + (n 1)dWhat is a1?a1 = 2What is the common difference?d = 3Now plug it into the formula to find the general term.an = 2 + (n 1)3an = 2 + 3n 3an = 3n - 1Now find the 13th term (n = 13).a13 = 3(13) 1 = 38Arithmetic SequencesYour turn!Find the 10th term of the sequence 3, 10, 17, 24, an = 7n 4a10 = 66

Find the 19th term of the sequence 7, 1, -5, -11, an = -6n + 13a19 = -101Arithmetic SequencesArithmetic SequencesRemember, I have an issue with how this shows up. Your homework has the correct form.Arithmetic SequencesArithmetic SequencesIn this case, to find n you must find the general term first.an = 4 + (n 1)3 = 4 + 3n 3an = 3n +1151 = 3n + 1150 = 3nn = 50Arithmetic SequencesApplication problemsJack and Jill both graduated from college with a degree in English. Jack got a job as a high school teacher making $35,000 in the first year with a $500 raise every year after that. Jill got a job as an editor of a newspaper. Her salary is $45,000 per year with a $1,000 raise each year. How much will each of them make in 10 years?Summation!!Jacka1 = 35,000d = 500n = 10an = 500n + 34500a10 = 39500S10 = $372,500Jilla1 = 45,000d = 1000n = 10an = 1000n + 44000a10 = 54000S10 = $495,000