 # Recursive and Explicit Formulas for Arithmetic Linear Sequences

• Slides: 11 Recursive and Explicit Formulas for Arithmetic (Linear) Sequences Objective: Students will be able to write the recursive and explicit forms of arithmetic sequences. Essential Questions: For arithmetic sequences, how do you convert recursive form to explicit form? For arithmetic sequences, how do you convert explicit form to recursive form? Identify the first term and the common difference of each arithmetic sequence. BE CAREFUL: ALWAYS CHECK TO MAKE SURE THE DIFFERENCE IS THE SAME BETWEEN EACH TERM ! Identify the first term and the common difference of each arithmetic sequence. BE CAREFUL: ALWAYS CHECK TO MAKE SURE THE DIFFERENCE IS THE SAME BETWEEN EACH TERM ! A recursive formula for a sequence would be: a 1= first term in the sequence an = term you are trying to find an-1 = previous term in the sequence d = common difference Find the first four terms given the following information. Make sure to derive the general formula. a) The first term is 3 and the common difference is - 4 b) The first term is 8 and the common difference is 3 Explicit Formulas A formula that allows you to find the nth term of the sequence by substituting known values in the expression. An explicit formula for sequence would be: an = d( n - 1) + a 1= first term in the sequence an = current term in the sequence d = common difference n = term number In the sequence 10, 40, 70, 100, …. The common difference between the terms is The first term of the sequence is The explicit formula for this sequence would be: an = 10 + 30( n - 1) which simplifies to: an = -20 + 30 n **I plugged in 10 for the first term and 30 for the constant difference and distributed** Write the explicit formula of the sequence 4, 7, 10, 13, …. In the sequence 4, 7, 10, 13, …. To find the 11 th term explicitly, I plug in the into the formula I just made: an = 1 + 3 n a 11 = 1 + 3(11) a 11 = 34 Find the 15 th term of the sequence using the formula: an = 1 + 3 n a 15 = 1 + 3(15) a 15 = 46 Example Test Question The first row of theater has 15 seats in it. Each subsequent row has 3 more seats than the previous row. If the last row has 78 seats, how many rows are in theater? Converting Between Formulas Recursive to Explicit Write the explicit formula for this sequence. a 1 = - 22 an = an-1 + 7 Write the explicit formula for this sequence. a 1 = 8 an = an-1 – 13 Converting Between Formulas Explicit to Recursive Write the recursive formula for this sequence. an = 12 n – 7 Write the recursive formula for this sequence. an = - 3 – 8 n