Sequences and S...

Let \(T_ r\) be the \(r\)th term of an AP, for \(r=1,2,3, \ldots\) If for some positive integers \(m , n\), we have \(T_m =\frac{1 }{ n}\) and \(T_n =\frac{1 }{ m}\), then \(T_{m n}\) equals:

If the first term minus the third term of a GP is 768 and the third term minus the seventh term of the same GP is 240, then what is the product of the first 21 terms?

If the sum of three numbers in A.P is 24 and their product is 440, find the numbers.

If a, b, c are in AP then (ac)² equals to:

The middle term of A.P. 5, 12, 19, ..., 215 is:

If \(y=x+x^{2}+x^{3}+\ldots\) up to infinite terms where \(x<1\), then which one of the following is correct?

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in AP. The common ratio of GP is:

The sum of n terms of two AP's are in the ratio of  (3n + 8) : (7n + 15). Find the ratio of their 12^th terms.

If the arithmetic mean and the geometric mean of two numbers are 13 and 12 respectively, then the two numbers are:

The third term of a geometric progression (GP) is 2. The product of the first 5 terms is: