Question

Which one of the following recursive formulas represents the same geometric sequence as the formula

Answer 1

i think its a but im not sure

Answer 2

The recursive formula that is used to represent the same geometric sequence as formula is:

`a_1=2`

and
`a_n=a_(n-1)\cdot (1)/(2)`

Explanation:

We are given a formula as:

`a_n=2\cdot ((1)/(2))^(n-1)`

Now, the first term of it is given by:

`a_1=2* ((1)/(2))^(1-1)\\\\\\a_1=2* ((1)/(2))^0\\\\\\a_1=2`

Also,
`a_2=2\cdot ((1)/(2))^(2-1)\\\\\\a_2=2\cdot ((1)/(2))\\\\\\a_2=a_1\cdot (1)/(2)`

and similarly we get:

`a_3=2\cdot ((1)/(2))^(3-1)\\\\\\a_3=2\cdot (1)/(2)\cdot (1)/(2)\\\\\\a_3=a_2\cdot (1)/(2)`

Hence, option: C is the correct answer.