If n arithmetic means are inserted between 2 and 38 then the sum of the resulting series is obtained as 200 . Then find the value of n.

n arithmetic means are inserted between x and 2y and then between 2x and y . If the rth means in each case be equal then find the ratio x/y.

Insert 6 arithmetic means between 3 and 24.

If the sum of first n terms of an arithemetic progression 2,5,8… is equal to sum of the first n terms of another arithmetic progression 57,59,61.. Then find the value of n

Find the sum of the following series upto n terms 0.6+0.66+0.666+ …

If (n!)/((n-2)!)=56 , find the value of n

Find the sum of the first n-terms of the series. 2+22+222+…..

n, 3n, 5n,... is an arithmetic sequence. a) What is the common difference? b) Prove that the sum of first 'n' terms of this sequence is n^(3) . c) Then find the sum of 15 terms of the sequence 15,45,75,…..

Find the sum of the first n terms of the series whose nth term is n(n+3) .

If the sum of n terms of an A.P is 3n^2+5n and its m^(th) term is 164. Find the value of m.