Find the 6th term from the end of the list of numbers 3, -6, 12, -24, …. , 12288.

The given list of numbers 3, -6, 12, -24, …. , 12288 is a G.P. with last term = l = 12288 and the common ratio = r = -2.

By formula, nth term from end = $l\Big(\dfrac{1}{r}\Big)^{n - 1}$

$\text{7th term from end } = 12288\Big(-\dfrac{1}{2}\Big)^{6 - 1} \\[1em] = 12288\Big(-\dfrac{1}{2}\Big)^5 \\[1em] = -\dfrac{12288}{32} \\[1em] = -384.$

Hence, the 6th term from end of the G.P. is -384.