The latest challenge in my daughter's Honor's Algebra Class is this problem.

The pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd letter in the pattern? Please help, I am trying to figure out.

Warm Regards,



Hi Patty,

Let me do a slightly different, but similar problem.

The decimal expansion of 1/7 is

 1/7 = 0.142957142957...

and the pattern repeats. What is the 500th digit in the decimal expansion of 1/7?

The pattern here is 6 characters long. 142957 Imagine that you have the 500 digits in front of you.How many times does the pattern 142957 repeat?

 500/6 = 83 with a remainder of 2

Thus the pattern repeats 83 times (that is 683 = 498 digits) and then there are two more digits, 14. Thus the 500th digit in the decimal expansion of 1/7 is 4.

Doed this help?



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