Sequences and Series
Let an= product of the first n natural numbers. Then for all n ϵ N
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Show that the products of the corresponding terms of the sequences a, ar,ar2,,˙˙˙arn−1and A,AR,AR2,,˙˙˙ARn−1,form a G.P, and find the common ratio.
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
Show that the sum of (m+n)thand (m−n)thterms of an A.P. is equal to twice the mthterm.
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Find the sum to n terms of the series :1×21+2×31+3×41+˙˙˙
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?
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.