Question

Find the next term of the geometric sequence:

4096, 1024, 256, 64, 16…

• A. 6
• B. 5
• C. 4
• D. Not a geometric sequence

Answer 1

The correct option is C 4

The given sequence is 4096, 1024, 256, 64, 16…

Let us divide each term in the above sequence by the term preceding it.

$1024÷4096=\frac{1}{4}$

$256÷1024=\frac{1}{4}$

$64÷256=\frac{1}{4}$

$64÷256=\frac{1}{4}$

$16÷64=\frac{1}{4}$

We observe that in the above sequence the each term is $\frac{1}{4}$ times the term preceding it.

So, the next term in the sequence = $16\times \frac{1}{4}=4$