What is the recursive formula for the geometric sequence with this explicit formula an=9*(-1/3)^(n-1)

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

where,

is the first term

r is the common ratio to the following terms.

As per the statement:

Given the explicit formula for geometric sequence:

On comparing with [1] we have;

and

The recursive formula for geometric sequence is given by:

Substitute the given values we have;

Therefore, the recursive formula for the geometric sequence is,

a_0 = -27

a_n = a_(n-1) * (-1/3)

Step-by-step explanation:

First evaluate given formula at n=0 and specify that as starting value

Then find how to get from n-1 to n by comparing two values. In this case the next value is formed by multiplying by -1/3.

Hello from MrBillDoesMath!

See Discussion below

Discussion:

A function f is even if f(-x) = f(x)

f(x)                               f(-x)                                  Are they equal?

-x^8 + 2x^6-5x           -(-x)^8 + 2(-x)^6 + 5x         No

3 abs(x) - 4                 3 abs(-x) -4                       Yes

log5 x^2                     log5 (-x)^2                        Yes

(6x)^ (1/7)                     (-6x)^(1/7)                          No

e^(x^2-x)                     e^( (-x)^2+x)                      No

(x^8 +5x^2)^(-1)           ( (-x)^8 + 5 (-x)^2) ^(-1)      Yes

Answers with Yes, above are even functions.

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!