Question

State the geometric sequence both recursive and explicit formulas.

Answer 1

here you go i hope this helps you out :)

Answer 2

recursive formula =
`a_(n) = a_(n-1)* r`

explicit formula:
`a_(n) = a_(1)*r^(n-1)`

Explanation:

Thinking process:

Let a sequence be given as:

3 9 27 81

As can be observed from the sequence, the next number of the sequence is a multiple of 3, that is 9 is a multiple of 3. Similarly, 27 is 9 multiplied by 3

then, let the first term be a. the common multiplying factor will be r (in this case 3). Then the formula will be
`a_(n) = a_(n-1)*r`

In addition, the powers rule applies.

For instance:

9 =
`3^(2)`

27 =
`3^(3)`

81 =
`3^(4)`

Then the explicit formula will be
`a_(n) = a_(1)*r^(n-1)`