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Arithmetic Sequences

Arithmetic Sequences. Part 2. Arithmetic Sequences. Remember 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: a n = a 1 + (n – 1)d. Arithmetic Sequences.

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Arithmetic Sequences

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  1. Arithmetic Sequences Part 2

  2. Arithmetic Sequences • Remember 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)d

  3. Arithmetic Sequences • Now 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)d • What is a1? • a1 = 2 • What is the common difference? • d = 3 • Now plug it into the formula to find the general term. • an = 2 + (n – 1)3 • an = 2 + 3n – 3 • an = 3n - 1 • Now find the 13th term (n = 13). • a13 = 3(13) – 1 • = 38

  4. Arithmetic Sequences • Your turn! • Find the 10th term of the sequence 3, 10, 17, 24, … • an = 7n – 4 • a10 = 66 • Find the 19th term of the sequence 7, 1, -5, -11, … • an = -6n + 13 • a19 = -101

  5. Arithmetic Sequences • Now we will find the sum of an arithmetic sequence. • Remember the sum is the sum of the stated terms in the sequence. • Use the next formula on your sheet for this: • Sn = (a1 + an) • n is the number of terms being added. • a1 is the first term in the sequence • an is the last number in the sequence.

  6. Arithmetic Sequences • Find the sum of the arithmetic sequence. • Sn = (a1 + an) • n = 100 • a1 = 1 • an = 100 • S100 = 1 +100) • = 50 (101) • = 5050 Remember, I have an issue with how this shows up. Your homework has the correct form.

  7. Arithmetic Sequences • Try another one. • n = 30 • a1 = 5 • a30 = 63 • S30 = (5 + 63) • = 15(68) • = 1020

  8. Arithmetic Sequences • Try these: • n = 13 • a1 = -7 • a15 = -31 • S15 = -247 • 4 + 7 +10 + … + 151 • a1 = 4 • an = 151 • n = ?? • S50 = 3875 In this case, to find n you must find the general term first. an = 4 + (n – 1)3 = 4 + 3n – 3 an = 3n +1 151 = 3n + 1 150 = 3n n = 50

  9. Arithmetic Sequences • Application problems • Jack 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!! • Jack • a1 = 35,000 • d = 500 • n = 10 • an = 500n + 34500 • a10 = 39500 • S10 = $372,500 • Jill • a1 = 45,000 • d = 1000 • n = 10 • an = 1000n + 44000 • a10 = 54000 • S10 = $495,000

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