How many terms of the series `1+2+2^2+…..` must be taken to make 511?

How many terms of the series 15+12+9+... must be taken to make 15? Explain the double answer.

How many terms of the series 54 + 51 + 48 + … must be taken to make 513 ? Explain ? Explain the -double anwer.

How many terms of the series 2+6+18+ ... Must be taken to make the sum equal to 728 ?

How many terms of the series –12, – 9, – 6,... must be taken that the sum may be 54?

How many terms of the AP 20,19""1/3,18""2/3 ,…., must be taken to make the sum 300 ? Explain the double answer.