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Task 6 Number Patterns revision.docx Task 6 Finite Mathematics Task 6: Number Patterns

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Task 6 Number Patterns revision.docx Task 6 Finite Mathematics Task 6: Number Patterns A. Provide the first five terms of an arithmetic or geometric sequence that has a first term higher than 10 and a common differen ...

Task 6 Number Patterns revision.docx Task 6 Finite Mathematics Task 6: Number Patterns A. Provide the first five terms of an arithmetic or geometric sequence that has a first term higher than 10 and a common difference or ratio that is positive but not 1. a1= 15, a2=20, a3=25, a 4=30, a5 =35 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. an =a1 +( n âˆ’1 ) d an =15 +( nâˆ’1 ) ( 5 ) an =15 +5 nâˆ’5 an =5 n+10 2. Find the 30th term of the sequence from part A, using the nth term formula from part A1 and showing all work. an =a1 +( n âˆ’1 ) d a30=5 ( 30 )+10 an =15 +( nâˆ’1 ) ( 5 ) a30=150 + 10 an =15 +5 nâˆ’5 a30=160 an =5 n+10 B. Explain how to use patterns or sequences to determine the last digit of the number 7N, where N is the four-digit year of your birth. In determining the last digit of the number 7 N , I have to first substitute my birth year into the equation for N. The problem will now read 71979 . I would first try to figure out A pattern that would help me to determine what the last digit could be. I would start from the very first number and work my way through the line until I seen a pattern. 71=7 72= 4 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. . . . . . . . . . . . . . . . . . .. . . . .

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