Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem29

Levels 11&12 Video Solutions 2013 problem29

Video Transcription

Video Summary

Julian's algorithm generates a sequence using a recursive formula. By setting \( n = 1 \), the recursive formula becomes \( a_{m+1} = a_m + m + 1 \). To find the 100th element, \( a_{100} \), you calculate the sum of the first 100 positive integers. Using the formula \( \frac{n(n+1)}{2} \), where \( n = 100 \), the sum is 5050. The process involves verifying that this formulation satisfies the original expression \( a_{m+n} = a_m + a_n + mn \), which it does, confirming the solution is correct. The answer is 5050.

Keywords

Julian's algorithm

recursive formula

sequence

sum of integers

5050