Sequences and Series
What is the minimum value of
cos2a2+sin2xb2 where a >0 and b>0 ?
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Figure). In how may rows are the 200 logs placed and how many logs are in the top row?
If a, b, c are in A.P., b, c, d are in G.P. and c1,d1,e1are in A.P. prove that a, c, e are in G.P.
In a factory, 150 workers were engaged to finish a piece of work in a certain number of days. However, if 4 workers are dropped everyday, except the first day, it will take 8 more days to finish the work. Find the number of days in which the work was to be completed.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.