Question

Consider the following sequence: 1/6, 1/12, 1/24, 1/48, …. Find a15

Answer 1

Sequence:

`(1)/(6),(1)/(12),(1)/(24),(1)/(48),\ldots`

As we can see, the denominator of each term is multiplied times 2:

`6*2=12`
`12*2=24`
`24*2=48`

However, this can also be written as follows:

`6*2^1=12`
`6*2^2=24`
`6*2^3=48`

Thus, the formula for our sequence is:

`a_n=(1)/(6*2^n)`

As we are asked for a15, we have to replace the values:

`a_(15)=(1)/(6*2^(15))`

Simplifying:

`a_(15)=(1)/(196608)`

Answer:

`a_(15)=(1)/(196608)`