IIMB 2002 (QA) PYQs

If six arithmetic means are inserted between 3 and $\frac{13}{2}$, the ratio of the fifth and the first mean is:

Solve:

$\dfrac{1}{1\times2\times3\times4}+\dfrac{1}{2\times3\times4\times5}+\dfrac{1}{3\times4\times5\times6}+\cdots+\dfrac{1}{15\times16\times17\times18}$

If $x+\frac{1}{yz}$, $y+\frac{1}{zx}$, $z+\frac{1}{xy}$ are in A.P. then $x,y,z$ are in