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,
Patty
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 6
83
= 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?
Penny