Sequences and Series
There are n Arithmetic means between 13 and 61. If ratio of the first A.M. and (n−1) the A.M. may be 16:55, then find n.
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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 Fibonacci sequence is defined by 1=a1=a2 and an=an−1+an−2,n>2. Find anan+1,for n = 1, 2, 3, 4, 5.
Write the first five terms of the sequence whose nthterms are : an=n+1n
Insert two number between 3 and 81 so that the resulting sequence is G.P.
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?
Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that pa(q−r)+qb(r−p)+rc(p−q)=0
If pth, qth, rthand sthterms of an A.P. are in G.P. then show that(p−q), (q−r), (r−s)are also in G.P.
Find the sum to n terms of the series :1×2×3+2×3×4+3×4×5+˙˙˙