Question

Please explain how you got the question because i have no idea how to plug in the numbers

Answer 1

Given sequence:

`(1)/(2),\text{ }1,\text{ }(3)/(2),2`

To find the 109th term, we need to first determine whether the sequence follows an arithmetic progression or a geometric progression.

Check

The sequence is arithmetic if the successive terms of the sequence are formed by adding or subtracting a value.

The sequence is geometric if the successive terms of the sequence are formed by multiplying or dividing by a value.

We have that:

first term = 1/2

second term = 1

third term = 3/2

Taking the difference of the second term from the first term:

`\begin{gathered} =\text{ 1-}(1)/(2) \\ \text{ = }(1)/(2) \end{gathered}`

Taking the difference of the third term from the second term: