Two infinite geometric series starts from the same number. If the common ratios are 0.85 and 0.55 respectively, show that the sum of the first series is three times that of the second.

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Consider an infinite geometric series with first term a and common ratio r, if its sum is 4 and the second term is 3/4 then

The sum of some terms of G. P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

The sum of an infinite geometric series with positive terms is 3 and the sums of the cubes of its terms is (27)/(19) . Then the common ratio of this series is

Two particles are projected in air with speed v_0 at angles theta_1 and theta_2 (both acute) to the horizontal , respectively. If the height reached by the first particle is greater than that of the second, then which are the correct choices ?

The sum of an infinite geometric series is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then which of the following is not a possible first term? 108 b. 144 c. 160 d. none of these

Two groups are competing for the positions of the board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product is introduced was by the second group.

The sum of an infinite geometric series is 6 and the sum of its first two terms is (9)/(2) , find its common ratio.