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arithmetic Sequence: A sequence of numbers where the common difference occurs at level D1 Given the terms of a sequence. The first term, t1, is referred to as a. The common difference is referred to as d. 1. To determine the common difference, d, subtract backwards. 2. To determine the equation or formula for a sequence of numbers, determine a and d, and substitute into the general formula, tn a (n 1)d Given two non-consecutive terms. 3. To determine the equation or formula if given only two terms. Use tn and n to substitute into the general formula to create two linear equations. Solve the system of equations to determine a and d. 4. To determine the value of x if three algebraic terms are provided. Subtract backwards to find the two algebraic forms of D1. Equate the two differences and then solve for x. Using the TI Calculator. Linear Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 5 4 7 5 9 Using the calculator to determine the equation 1. First reset your calculator. Press 2nd, +, Reset, All Ram, Enter, Reset, Enter. 2. Turn Diagnostics ON. This will determine the percentage of fit. Press 2nd , 0, arrow down to Diagnostics ON, Enter, Enter. Using the TI Calculator. Linear Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 5 4 7 5 9 3. Press Stat, Enter. Enter term #’s in List 1. Arrow over to List 2 and enter Term Values. Using the TI Calculator. Linear Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 5 4 7 5 9 4. Press Stat. Arrow over to Calc. Scroll down to Lin Reg (ax+b). Hit ENTER. So, the equation of the sequence is t n 2n 1 100% match Q 4 3 2 1 −6 −4 −2−1 −2 −3 −4 y adratic Sequence: A sequence of numbers x 2 4 6 where the common difference occurs at level D2 Given the terms of a sequence. The power of the sequence is 2. 1. To determine the common difference, d, subtract backwards. 2. The general formula for the nth term of a Quadratic 2 Sequence is t n an bn c 3. To determine the equation or formula for a quadratic sequence, use the following formulas. D2 2a 3a b 1st term in D1 a b c 1st term in Sequence Given non-consecutive terms. 3. What if n doesn’t increase by just 1 unit? e.g. Term # Number 2 2 4 8 6 22 8 44 10 74 Let’s go back to the algebraic determination of the relationship between 2 D2 and “a”. t2 a(2) b(2) c 4a 2b c t4 a(4) 2 b(4) c 16a 4b c t6 a(6) 2 b(6) c 36a 6b c SEQUENCE 4a 2b c, 16a 4b c, 12a 2b 36a 6b c 20a 2b 8a In this case, D2 8a (22 ) * 2a (inc 2 ) * 2a 12a+2b= 1st term in D1 and 4a+2b+c= 1st term in sequence. Using the TI Calculator. Quadratic Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 6 4 10 5 15 Using the calculator to determine the equation 1. First reset your calculator. Press 2nd, +, Reset, All Ram, Enter, Reset, Enter. 2. Turn Diagnostics ON. This will determine the percentage of fit. Press 2nd , 0, arrow down to Diagnostics ON, Enter, Enter. Using the TI Calculator. Linear Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 6 4 10 5 15 3. Press Stat, Enter. Enter term #’s in List 1. Arrow over to List 2 and enter Term Values. Using the TI Calculator. Linear Regression: The process of determining the line of best fit. Term # Number 1 1 2 3 3 6 4 10 5 15 4. Press Stat. Arrow over to Calc. Scroll down to Quad Reg. Hit ENTER. 100% match So, the equation of the sequence is tn 1 2 1 n n 2 2