Question

Which number comes next in this series? 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, ?

Answer 1

This is a geometric sequence, with the first term: 1/64

The common ratio is found through the ratio of the first two terms and the second and third term.
$\frac{\frac{1}{32}}{\frac{1}{64}} = \frac{\frac{1}{16}}{\frac{1}{32}}$
$\frac{1}{32} \cdot 64 = \frac{1}{16} \cdot 32$

Since there is a common difference of 2, we can generalise this sequence to find the nth term:
$T_n = ar^{n-1}$
a is the first term, r is the common ratio, and n is the nth term in the sequence.

$T_n = \frac{1}{64} \cdot 2^{n-1}$
Substituting n = 7, we get:
$T_7 = \frac{1}{64} \cdot 2^{7 - 1}$
$T_7 = \frac{1}{64} \cdot 64$
$T_7 = \frac{64}{64} = 1$

Thus, the next term in the sequence is 1.