S₁ is a series of 4 consecutive even numbers. If the sum of reciprocal of first two numbers of S₁ is 11/60, then what is the reciprocal of third highest number of S₁

Let 4 consecutive even number is

x, x+ 2, x+ 4, x+ 6

$frac{1}{x} + frac{1}{{x + 2}} = frac{{11}}{{60}}$

$frac{{x + 2 + x}}{{xleft( {x + 2} ight)}} = frac{{11}}{{60}}$

$frac{{2left( {x + 1} ight)}}{{{x^2} + 2x}} = frac{{11}}{{60}}$

$120x + 120 = 11{x^2} + 22x$

$11{x^2} - 98x - 120 = 0$

$x = frac{{ - 24}}{{22}},10 = - frac{{12}}{{11}},10$

∴ third highest number is 12 and

reciprocal 3rd highest no. is $frac{1}{{12}}$