The second term of a geometric series is 3 and the common ratio is . Find the sum of

first 23 consecutive terms in the given geometric series.

Find the sum of the following finite series

(i) 1 + 0.1 + 0.01 + 0.001 + … + ( 0.1)9 (ii) 1 + 11 + 111 + … to 20 terms.

How many consecutive terms starting from the first term of the series

(i) 3 + 9 + 27 + … would sum to 1092 ? (ii) 2 + 6 + 18 + … would sum to 728 ?

A geometric series consists of four terms and has a positive common ratio. The sum of the first two terms is 9 and sum of the last two terms is 36. Find the series.

Find the sum of first n terms of the series

(i) 7 + 77 + 777 + … . (ii) 0.4 + 0.94 + 0.994 + … .