Question

Which sequence can be generated from the formula f(x + 1) = {(f(x))?Ox x0 x..…,2' 4'6O x, 2x, 4x, 8x, ...0 x .4'O x, 2x, 4x, 6x, ...

Answer 1

its C

Explanation:

Answer 2

Concept:

We will first have to calculate the common ratio of the sequence and see the sequence that gives a common ratio of 1/2

From the first option

The formula given in the question is given below as

`\begin{gathered} f(x+1)=(1)/(2)f(x) \\ (f(x+1))/(f(x))=(1)/(2) \end{gathered}`

From the first option,

`\begin{gathered} r=(T_2)/(T_1)=((x)/(2))/(x)=(1)/(2) \\ r=(T_3)/(T_2)=((x)/(4))/((x)/(2))=(x)/(4)*(2)/(x)=(1)/(2) \\ r=(T_4)/(T_3)=((x)/(6))/((x)/(4))=(x)/(6)*(4)/(x)=(2)/(3)(wrong) \end{gathered}`

Hence,

The first option is wrong

From the second option,

`\begin{gathered} r=(T_2)/(T_1)=(2x)/(x)=2 \\ r=(T_3)/(T_2)=(4x)/(2x)=2 \\ r=(T_4)/(T_3)=(8x)/(4x)=2(\text{wrong)} \end{gathered}`

Hence,

The second option is wrong

From the third option,

`\begin{gathered} r=(T_2)/(T_1)=((x)/(2))/(x)=(1)/(2) \\ r=(T_3)/(T_2)=((x)/(4))/((x)/(2))=(x)/(4)*(2)/(x)=(1)/(2) \\ r=(T_4)/(T_3)=((x)/(8))/((x)/(4))=(x)/(8)*(4)/(x)=(1)/(2)(correct) \end{gathered}`

Hence,

The right answer is the third option

`x,(x)/(2),(x)/(4),(x)/(8)`