If $\mathrm{S}_{\mathrm{n}}=4+11+21+34+50+$ $\_\_\_\_$ to n terms, then $\frac{1}{60}\left(\mathrm{~S}_{29}-\mathrm{S}_9\right)$ is equal to

Let $a_1, a_2, a_{3, \ldots . .}$ be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2...

Let an be the nth term of the series 5 + 8 + 14 + 23 + 35 + 50 + … and . Then$...

If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1+4 \cdot 1^4}+\frac{4 \cdot 2}{1+4 \cdot 2^4}+\frac{4 \cdot 3}{1+4 \cdot 3^4}+\ldots$. is...

$ \begin{aligned} & \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots \infty=\frac{\pi^4}{90} \\ & \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots \infty=\alpha, \\ & \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots \infty=\beta \end{aligned} $ then $\frac{\alpha}{\beta}$ is equal to

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth...

Let $a_n$ be the $n^n$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700, a_0=7$ and $S_7=7$, then $a_n$ is equal to:

The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even...

If the sum of the first 20 terms of the series $$ \frac{4 \cdot 1}{4+3 \cdot 1^2+1^4}+\frac{4 \cdot 2}{4+3 \cdot 2^2+2^4}+\frac{4 \cdot 3}{4+3 \cdot 3^2+3^4}+\frac{4...

Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of $A$ be 36...