Exercise - 5.3

. Find the sum of the first -terms of the arithmetic progression having the sum of first terms as and the sum of the first terms as . . Find the sum up to the th term of the series + + + + + + + + + · · · . Compute the sum of first n terms of the following series: i. + + + + · · · ii. + + + + · · · . Compute the sum of first n terms of + ( + ) + ( + + ) + ( + + + ) + · · · . Find the general term and sum to n terms of the sequence , , , , . . . . . Find the value of n , if the sum to n terms of the series + + + · · · is . . Show that the sum of ( m + n ) th and ( m − n ) th term of an AP. is equal to twice the m th term. . A man repays an amount of Rs. by paying Rs. in the first month and then increases the payment by Rs. per month. How long will it take him to clear the amount? . In a race, balls are placed in a line at intervals of meters, with the first ball meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls? . The number of bacteria in a certain culture doubles every hour. If there were bacteria present in the culture originally, how many bacteria will be present at the end of nd hour, th hour and n th hour? . What will Rs. amounts to in years after its deposit in a bank which pays annual interest rate of % compounded annually? . In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being particles on the first day. Find the day when the infectious virus particles just grow over , , units? . .