Answer:
Checkmark:
✓ The sequence is geometric
✓ The recursive formula for the sequence is [tex]An = A_{n-1}(-3)[/tex]; [tex]A_{1} =-2[/tex]
✓ The explicit formula for the sequence is [tex]t_{n} = (-2) (-3)^{n-1}[/tex]
Step-by-step 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
[tex]t_{n} = t_{1} r^{n-1}[/tex]
[tex]t_{1}[/tex] = -2
Substitute the values in the equation:
[tex]t_{n} = (-2) (-3)^{n-1}[/tex]
This is a explicit formula since the next value depends on the position of n (1, 2, 3 .etc)
The recursive formula would be:
[tex]An = A_{n-1}(-3)[/tex]
Checkmark:
✓ The sequence is geometric
✓ The recursive formula for the sequence is [tex]An = A_{n-1}(-3)[/tex]; [tex]A_{1} =-2[/tex]
✓ The explicit formula for the sequence is [tex]t_{n} = (-2) (-3)^{n-1}[/tex]
