# Arithmetic Sequences & Series Pre-Calculus Section.

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Arithmetic Sequences & Series Pre-Calculus Section

It is an “Arithmetic Sequence” when the same number is added to get from one term to the next. The number being added is called the common difference (d). To find d: ( a 2 - a 1 ), or (a 3 - a 2 ), or (a 4 - a 3 ), etc. 1. 18, 12, 6, 0, - 6,… d = __ - 6 2. - 13, - 6, 1, 8, … d = __ 7 To find the common difference, subtract any two consecutive terms.

1) Decide if each series is an arithmetic series. If so, find the common difference. Yes, difference = 4. 2) No common difference. 3) No common difference. 4) Yes, difference = -4.

If the 1st term of an arithmetic sequence is 10, & the common difference is 3, find the next 4 terms. a 1 = 10a 2 = _____ = __13 a 3 = ______ = __ 16 a 4 = __19 a 5 = __22 10 + d13 + d If the first term of an arithmetic sequence is 6, & the common difference is -2, find the first 4 terms. a 1 = __, a 2 = __, a 3 = __, a 4 = __6 4 2 0 13, 16, 19, 22 6, 4, 2, 0

- 112 Given the sequence: 8, 5, 2, - 1, …, find the 41st term. Formula to find a specific term: a n = a 1 + (n - 1)d a n = the term to be found a 1 = 1st term n = number of terms d = common difference 841a 41 = ____ a 1 = __n = __ d = __ - 3 a 41 =_________8+ 40(- 3) Memorize This Formula!

a 15 = _________ = ____ 6 + 14(- 3) - 36 Find the 15 th term of the sequence: 6, 3, 0, … a 1 = __; d = __; n = __ In an arithmetic sequence, a 1 = 2; d = 3; find a 10 6 - 315 10 a 10 = _______ = ___2 + 9(3)29 a n = a 1 + (n - 1)d a 1 = __; d = __; n = __32 a n = a 1 + (n - 1)d

1) 2)

a n = a 1 + (n - 1)d Need to know the 1 st term. Find it first!

a n = a 1 + (n - 1)d

Sum of a Finite Arithmetic Sequence To use this formula, you must know the first and the last term. Alternate Formula To use this formula, you must know the first term and the common difference.

n = 20 a 1 = 12 d = 6

Find the 50 th term. a n = a 1 + (n - 1)d

We don’t know how many terms are being added! First find what term 38 is. a n = a 1 + (n - 1)d 38 = 3 + (n – 1)5 38 = 3 + 5n – 5 38 = 5n – 2 40 = 5n 8 = n It’s the 8 th term!

Formulas to Memorize! a n = a 1 + (n - 1)d Write the formula at the beginning of each problem. You will have it memorized by the time you finish the homework.

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