Finite Mathematics JZM1 task 6.docx JZM1 – Finite Mathematics Task 6: Number Patter

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Finite Mathematics JZM1 task 6.docx JZM1 – Finite Mathematics Task 6: Number Patterns Part A: Provide the first five terms of an arithmetic or geometric sequence that has a first term hi... gher than 10 and a common difference or ratio that is positive but not 1. 13. 15, 17, 19, 21 Part A 1: Using the general formula for either the arithmetic or geometric sequence, derive the specific nth term formula for the sequence from part A, showing all steps. The general formula for an arithmetic sequence is = + (n -1)d. Since stands for the first term in the sequence, I used my youngest daughters age of 13. D is the common difference between two numbers in the pattern. Each number in my pattern increases by 2 each time. Therefore, 2 becomes the value of d. The nth formula for the pattern used above is: = 13 + (n – 1) 2. Part A 2: Find the 30th term of the sequence from part A, using the nth term formula from part A1 and showing all work. = 13 + (n – 1) 2 = 13 + (30 – 1) 2 = 13 + (29) 2 = 13 + 58 = 71 Part B: Explain how to use patterns or sequences to determine the last digit of the number, where N is the four-digit year of your birth. To begin, I will make a chart of 7 to nth powers to see if I can find a pattern or sequence. 7 to the nth power Resulting number 1 7 49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. . . . . . . . . . . . . . . . . . .. . . . . [Show More]

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