Group Activity Pair up with a partner to create a sequence recursively together
MATHEMATICS · Subjective · CBSE · Mathematics · Number Play · Number Play
Problem
41. Group Activity Pair up with a partner to create a sequence recursively together. Each of you picks five random digits from 1 to 9 (with repetitions, if you wish). Merge your digits to make a list of ten. Now each of you constructs a ten-digit number using exactly the numbers in your list.
Let a1= the (positive) difference between your two numbers.
Let an+1= the sum of the digits of an for n≥1.
This sequence converges, since it is eventually constant. What is the limit? (Remember, you can check your answer in the back of the book.)