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

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

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

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

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 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.

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.

Observe the number pattern made using terms of an arithmetic sequence 2, 6,10, ... . Write the next two lines.

In an A.P., the first term is 3 and the last term is 17. The sum of all the terms in the sequence is 70. Then the number of terms in the arithmetic sequence is

The harmonic mean between two numbers is 21/5 their A.M. A and G.M. satisfy the relation 3A+ G^(2) = 36 . Then find the sum of square of numbers .