141.

The sum of n terms of the series 1 + 5 + 12 + 22 + 35 + ... is

• $\frac{{\mathrm{n}}^2\left(\mathrm{n} + 1\right)}{8}$

• $\frac{{\mathrm{n}}^2\left(\mathrm{n} + 1\right)}{6}$

• $\frac{{\mathrm{n}}^2\left(\mathrm{n} + 1\right)}{2}$

• None of these

If geometric mean and harmonic mean of two numbers a and b are 16 and 64/5 respectively, then the value of a : b is

• 4 : 1

• 3 : 2

• 2 : 3

• 1 : 4

If the sum offour numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18, then the numbers are

• 3, 9, 27, 81

• 4, 8, 16, 32

• 2, 6, 18, 54

• None of these

iF a,b and c are in HP, then for any n $\in$ N, which one of the following is true ?

• aⁿ + cⁿ < 2bⁿ

• aⁿ + cⁿ > 2bⁿ

• aⁿ + cⁿ = 2bⁿ

• None of the above

The sum of the series $\frac{1}{2 . 3} + \frac{1}{4 . 5} + \frac{1}{6 . 7} + ...$ is

• $\log \left(\frac{\mathrm{e}}{2}\right)$

• $\log \left(\frac{2}{\mathrm{e}}\right)$

• $\frac{\mathrm{e}}{2}$

• $\frac{2}{\mathrm{e}}$

If $\frac{{\mathrm{a}}^{\mathrm{n} + 1} + {\mathrm{b}}^{\mathrm{n} + 1}}{{\mathrm{a}}^{\mathrm{n}} + {\mathrm{b}}^{\mathrm{n}}}$ be the AM of a and b, then n is equal to

• - 1

• 0

• 1

• None of these

x^1/2 . x^1/4 . x^1/8 ... $\infty$ equal to

• 0

• 1

• $\infty$

• x

If a, b, c are in arithmetic progression, then $\frac{\mathrm{a}}{\mathrm{bc}}, \frac{1}{\mathrm{c}}, \frac{2}{\mathrm{b}}$ will be in

• arithmetic proression

• geometric progression

• harmonic progresssion

• None of the above

If G is the geometric mean of x and y, then $\frac{1}{{\mathrm{G}}^2 - {\mathrm{x}}^2} + \frac{1}{{\mathrm{G}}^2 - {\mathrm{y}}^2}$ will be

• - G²

• $- \frac{1}{{\mathrm{G}}^2}$

• $\frac{1}{{\mathrm{G}}^2}$

• G²

If a > 1, b > 1 and c > 1 are in geometric progression, then $\frac{1}{1 + {\log }_{\mathrm{e}}\left(\mathrm{a}\right)}, \frac{{\displaystyle 1}}{{\displaystyle 1 + {\log }_{\mathrm{e}}\left(\mathrm{b}\right)}}, \frac{{\displaystyle 1}}{{\displaystyle 1 + {\log }_{\mathrm{e}}\left(\mathrm{c}\right)}}$ will be in

• arithmetic proression

• geometric progression

• harmonic progresssion

• None of the above