Question

Hello math olzzzzzzz

Answer 1

Checkmark:

✓ The sequence is geometric

✓ The recursive formula for the sequence is
`An = A_(n-1)(-3)`;
`A_(1) =-2`

✓ The explicit formula for the sequence is
`t_(n) = (-2) (-3)^(n-1)`

Explanation:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by -3 gives the next term.

r = -3

`t_(n) = t_(1) r^(n-1)`

`t_(1)` = -2

Substitute the values in the equation:

`t_(n) = (-2) (-3)^(n-1)`

This is a explicit formula since the next value depends on the position of n (1, 2, 3 .etc)

The recursive formula would be:

`An = A_(n-1)(-3)`

Checkmark:

✓ The sequence is geometric

✓ The recursive formula for the sequence is
`An = A_(n-1)(-3)`;
`A_(1) =-2`

✓ The explicit formula for the sequence is
`t_(n) = (-2) (-3)^(n-1)`