Insert five numbers between 8 and 26 such that the resulting sequence is an AP.

Insert three numbers between 1 and 256 so that the resulting sequence is a GP.

Insert two numbers between 3 and 81 so that the resulting sequence is a G.P.

Insert two numbers between 3 and 81 iso that the resulting sequence is G . P

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^(th) and (m-1)^(th) numbers in 5:9. Find the value of m.

Insert three A.M.s between 11 and 14

Insert 6 arithmetic means between 3 and 24.

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.

Insert 4 geometric means between 4 and 972.

Consider the numbers between 100 and 300 which leave remainder 2 on division by 3 a) Which is the first number in this sequençe? b) Which is the last number in this sequence? c). How many such numbers are there in this sequence? d) Find the, sum of all numbers in the sequence.