Problem
ALG-B1-M05-P005 Sum with Unknown Number of Terms
#5
★★☆☆☆ Level 2 of 5
Find the sum of all positive terms of \(53,48,43,\ldots\).
First find the last positive term.
The general term is \(a_n=53-5(n-1)\). Positivity gives \(58-5n>0\), so \(n\le11\). The last term is \(a_{11}=3\).
The sum is \(\frac{11(53+3)}2=308\).
The boundary must be controlled.