Sequences and S...

If the sum of n terms of an A.P. is given by

\(S_n = 3n + 2n ^2 \), then the common difference of the A.P. is

The third term of G.P. is 4. The product of its first 5 terms is

If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

Let \(S_n\) denote the sum of the first n terms of an A.P. If \(S_{2n}\) = \(3S_n\)then \(S_{3n}\) : \(S_n\) is equal to

The minimum value of \(4^x + 4^{1–x} , x \in R\), is

Let \(S_n\) denote the sum of the cubes of the first n natural numbers and \(s_n\) denote the sum of the first n natural numbers. Then \(\displaystyle\sum_{r=1}^{n}\frac{S_r}{s_r}\) equals

If \(t_n\) denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then \(t_{50}\) is

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 \(cm^3\) and the total surface area is 252\(cm^2\). The length of the longest edge is

If sum of n terms of a sequence is given by \(S_n = 2n^2 \) + 3n, find its 50th term.

Find the number of terms in the sequence 4, 12, 20, ........108.

Find the product of 11 terms in G.P. whose 6th is 5.

Find three numbers in G.P. having sum 19 and product 216.

Find the sum of the series to n terms whose general term is 2n + 1.