The maximum sum of the series 20+1913+1823+18+…is

The given series is arithmetic whose first term = 20, common difference = – . As the common difference is negative, the terms  will become negative after some stage. So the sum is maximum if only positive terms are added.Now, tn=20+(n−1)−23≥0 if 60−2(n−1)≥0 or  62≥2n or 31≥n∴ The first 31 terms are non-negative.∴ maximum sum=S31=3122×20+(31−1)−23=312(40−20)−310