SOLUTION: 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. 1.  Explain h

Algebra ->  Sequences-and-series -> SOLUTION: 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. 1.  Explain h      Log On


   

Question 1075584: 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.
1.  Explain how to determine the nth term formula.
2.  Find the 30th term, showing all work.
 
B.  Explain how to use patterns or sequences to determine the last digit of the number 7^N, where N is the four-digit year of your birth.
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
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B.  HINT:  the last digits of the sequence 7, 7%5E2, 7%5E3, 7%5E4, . . . 7%5En, . . .  n = 1, 2, 3, 4, 5, 6, 7, 8, . . . 

           form a periodic sequence 7, 9, 3, 1, 7, 9, 3, 1, . . . . 




So, if you were born in 2001, then the last digit of the number 7%5E2001 is 7;

    if you were born in 2002, then the last digit of the number 7%5E2002 is 9;

    if you were born in 2003, then the last digit of the number 7%5E2003 is 3;

    if you were born in 2004, then the last digit of the number 7%5E2004 is 1;


And so on . . . . cyclically . . .