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## Hand back quiz

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**Find the average rate of change.**f(x) = 2x2 + 5 when x1 = 1 and x2 = 3 m = 8**GPS Algebra**EQ: How do you write the rule for an arithmetic sequence? How do you find the 50th term? How do you compute the sum of an arithmetic series? MA1A3.d. Explore arithmetic series and various ways of computing their sums.**Sequences**The values in the range are called the terms of the sequence. Domain: 1 2 3 4…....n Range: a1 a2 a3 a4…..an A sequence can be specified by an equation or rule.**Find the first 5 Terms of the Sequence**an = 2n – 3 Find a1, a2, a3, a4, a5 a1 = -1 First Term a2 = 1 Second Term a3 = 3 Third Term a4 = 5 Fourth Term a5 = 7 Fifth Term**Find the first 5 Terms of the Sequence**an = n3 – 20 Find a1, a2, a3, a4, a5 a1 = First Term a2 = Second Term a3 = Third Term a4 = Fourth Term a5 = Fifth Term -19 -12 7 44 105**Arithmetic Sequences will have a constant common difference.****Tell whether the sequence 2, 11, 20, 29, 38, … is**arithmetic. Yes because each common difference is 9.**Tell whether the sequence 4, 8, 16, 22, 32, … is**arithmetic. No because the difference is not constant.**Arithmetic**Sequences**Write the rule**Example: 3, 5, 7, 9, ... an = 2n + 1**Write the rule**Example: 65, 60, 55, 50, ... an = -5n + 70**Write the rule**Example: 2, 6, 10, 14, … an = 4n – 2**What is the nth term?**a1 = 5 First Term a2 = 12 Second Term a3 = 19 Third Term a4 = 26 Fourth Term an = nth Term an= 7n – 2 What is the rule? an = ???**What is the 50th term?**Example: 1, 5, 9, 13, ... Substitute 50 in as an**What is the 18th term?**Example: 100, 93, 86, 79... Substitute 18 in as an**What is the 100th term?**Example: 4, 9, 14, 19... Substitute 100 in as an**Arithmetic Series**The expression formed by adding the terms of an arithmetic sequence**Find the sum of the arithmetic series**• Find the value of that nth term • Substitute values in to the arithmetic series formula**Find the sum of the arithmetic series**Find the sum of the first 50 terms: 3 + 6 + 9 + 12 + 15 + …**Find the sum of the arithmetic series**Find the sum of the first 19 terms: 2 + 3 + 4 + 5 + …**Find the sum of the arithmetic series**Find the sum of the first 100 terms: 25 + 35 + 45 + 55 + …**EOCT Practice**• 77 b) 81 • c) 84 d) 86**Find the 25th term of the sequence 7, 11, 15, 19, 23, ...**EOCT Practice • 103 b) 104 • c) 107 d) 111**Home Work**More Practice with Sequences & Sums Worksheet