Sequences and Series
The least value of 21+32cosec2θ+83sec2θ is
The sum of first three terms of a G.P. is 1039 and their product is 1. Find the common ratio and the terms.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Figure).A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?[Hint : To pick up the first potato and the second potato, the total distance (in metres) rim by a competitor is 2 x 5 + 2 x (5 + 3)]
Write the first three terms in each of the following sequences defined by the following:(i) an=2n+5 (ii) an=4n−3