Question

Find the next numbers in the pattern?
1/2, 1/4, 1/8, 1/16, …
Choices:

1/32, 1/64, 1/148

1/24, 1/32, 1/40

1/32, 1/48, 1/64

1/32, 1/64, 1/128

I'm really confused? I just need help figuring out the Common Difference etc.

Answer 1

the denominator is being multiplied by two each time

Answer 2

You are doubling the last number, so 1/2, double the 2, so its 4, so 1/4, double 4 and get 8, and so on, get it?

Answer 3

this is a geometric sequence so there is a common ratio
it can be found by dividing the second term with the first term
so the common ratio r=1/2
to find the next numbers, you have to multiply the previous number with the common ratio
so the answer will be:
1/32, 1/64, 1/128

Answer 4

\[a_{n} = \frac{ 1 }{ 2n }\]
\[a_{1} = \frac{ 1 }{ 2(1) } = \frac{ 1 }{ 2 }\]
\[a_{2} = \frac{ 1 }{ 2(2) } = \frac{ 1 }{ 4 }\]
\[a_{3} = \frac{ 1 }{ 2(3) } = \frac{ 1 }{ 8 }\]
Just continue and you will get the next of the sequence